Well, this is a complex narrative about which many articles and books have been written. To try to summarize these findings would be impossible here so a short answer is in order.

First, beware of the legendary- ideological nature of the narrative. It is meant to justify Israel’s conquest of Canaan later in the book of Joshua. This foundational tale would then explain to the readers the reason why the Canaanites had to be subjugated: it was because Noah had already cursed them through their ancestor Ham, whom the narrative describes twice as the father of Canaan. In the next chapter of Genesis the descendants of Noah’s sons are described. It is a map, a blueprint to humanity as these ancient writers understood it. And of course, it reflects the writer’s point of view which will always favor Shem, the ancestor of the Israelites.

Second, beware of the cultural-symbolic nature of the narrative. Nudity was a taboo in the ancient Israelite society, especially the nudity of one’s parents. To see one’s parents’ nudity had the connotation of sexual intimacy and at times even incest or rape. All of these things may be implicit in the narrative, though the text is not clear about any of them. It may just point at Ham’s lack of respect for his father’s sexual life which he indiscreetly witnesses, or participates in, and goes on to report to his brothers. Still, the text mentions that Ham had done something to Noah and here is where the reader can find room for speculation alongside some of the ideas proposed above.

This story is an etiology (an origin story) that explains  why the Israelites were able to take over the land and suppress the Canaanites.
 
Ham’s sin is that after seeing his father lying naked in the tent, he does not cover him  as would have been appropriate.   Instead, he tells his brothers thereby shaming him.
 
Some scholars think that the phrase “When Noah awoke from his wine and knew  that which his youngest son had done to him” suggests sexual impropriety because it does not say “what he saw” but “what he did.”   But one could also interpret that what he did was humiliate his father by informing the brothers of his nakedness.
 
Likely the story was told in two versions, one where Canaan is the one who sees his grandfather naked (or does something to him) and one where Ham sees his father naked.  The story conflates the two and  is inconsistent in carrying forth the name of the guilty party.  The reason for the story, however, is to state that the Canaanites are a cursed people because their eponymous ancestor, Canaan, was cursed.
 
Noah’s anger is probably a reflection of his feelings of shame.  He is taking out his anger at himself on someone else.  This is a psychological explanation, not a theological one.  But it reflects how a lot of us react.
 
Associating nakedness with shame is not universal.  Notions of what is shameful is culturally determined; it is not inborn.  Some traditional people living in hot humid climates were mostly and sometimes completely naked and felt no shame until other people imposed their cultural notions upon them.  The story reflects the cultures of the ancient Near East that frowned upon nakedness.  There are many places in the Bible where nakedness whether of people or the land are viewed negatively.     There are a few places in the Bible where one would expect a statement of shame in connection to nakedness where none is found.  When David sees Bathsheba bathing, there is nothing in the story that suggests that is shameful.  When the prophet confronts David, it is because David took someone who belonged to someone else (Bathsheba) but there is no statement connecting his sin with nakedness or seeing nakedness.  The Song of Songs describes naked human bodies without a sense of shame.   The Adam and Eve story is humorous.    They are naked but they do not know it.   When their eyes are opened, they see that they are naked and they are ashamed.  Why should they care?  They are husband and wife and no one else is around.   They expect to be exposed to something extraordinary when they eat the fruit but the only thing that they discover is that they are naked.  They are ashamed because their nakedness is a visual symbol of their disobedience.  Covering up their nakedness does not cover their disobedience.    
 
Japhet lives in the tents of Shem.  Japhet is not cursed.  There is room in the land for Japhet, but Shem is the superior son because Shem is the ancestor of Abraham who is the ancestor of the Israelites (and actually a lot of others, too, along the line of Hagar, Keturah, Esau, etc).

Descendents of Noah’s son Ham and his grandson Canaan, the non-Israelite inhabitants of the land of Canaan, are introduced to biblical narrative in Genesis shortly after the story of the flood. After disembarking from the ark, Genesis reports, Noah planted a vineyard, drank some of the wine, and became drunk.  Coming upon his father asleep and inebriated, Ham “saw the nakedness” (râ’âh ‘erwat) of his father, and told his two brothers outside. Shem and Japheth, the two righteous brothers, then entered the tent to intervene. Covering their father’s nakedness, they walked backwards so as to avoid looking at him. Genesis emphasizes this point: “Their faces were turned away, and they did not see their father’s nakedness.”

Awaking from sleep, Noah learned what had happened, and, in response, he cursed Ham’s son Canaan and blessed Shem and Japheth: “Cursed be Canaan; lowest of slaves shall he be to his brothers….[But] blessed by the LORD my God be Shem; and let Canaan be his slave. May God make space for Japheth, and let him live in the tents of Shem; and let Canaan be his slave” (NRSV). Apparently, viewing the nakedness of one’s father was such a terrible crime that perpetual slavery for one’s descendants was an appropriate punishment, beginning with Ham’s son Canaan and continuing forever, so long as there were Canaanites in the land.

Among other purposes, this story involving Ham, Canaan and Noah’s nakedness likely served as a justification for the later Israelite conquest of both the Canaanites and the Philistines: already from the time of Noah, Genesis suggests, the descendants of Shem (the Israelites) were destined to rule over the descendants of Ham (the Canaanites) and of Japheth (the Philistines), but whereas the Philistines would later be tolerated (they would live in Israel’s tents), the Canaanites would not be. Like their ancestor Ham, they are beyond redemption. “But what was so terrible about viewing Noah’s nakedness?” the reader asks. This is a good question: such behavior hardly seems offensive, at least initially. Moreover, why would Noah curse Canaan, Ham’s son, instead of Ham himself? Interpreters have been troubled by this odd passage for centuries, offering various solutions, some of which blame Noah as well as Ham and, by extension, Canaan. According to the vast majority of interpretations, some sort of sexual indiscretion must have been in view.

Reasoning that Ham must have either castrated or raped his father, late ancient rabbis developed an explanation of this story capable of accounting for both the curse of Canaan rather than Ham and the severity of Noah’s reaction. Since Ham made it impossible for his father to beget further sons, Noah appropriately denied him future sons, making Canaan and all his descendants into slaves rather than free men, who would be capable of passing on their property to others. Alternatively, the rabbis reasoned, perhaps Ham sexually abused his father and did not castrate him, though they were not sure why this behavior would result in the curse of Canaan.

Late ancient Christians offered a very different set of interpretations. From their perspective, Ham’s sin was not so much sexual as disrespectful: Ham laughed at his father’s nakedness and made fun of his father’s shame in public, prefiguring the ridicule Christ would face when dying on a cross. As the fourth-century bishop Methodius put it, “When overpowered by wine, [Noah] was mocked.” Assuming that Noah prefigured Christ, bishop Ambrose of Milan recalled the story to emphasize the importance of modesty: “Ham, Noah’s son, brought disgrace upon himself, for he laughed when he saw his father naked, but they who covered their father received the gift of a blessing.” Since Christians respect Christ’s flesh like Shem and Japheth respected the flesh of their father, Ambrose argued, they too will be blessed. Reluctant to imagine that Noah, a savior like Christ, had been raped or castrated, Christian interpreters offered comparatively mild interpretations of this passage. Still, they were also convinced that Ham—and by extension his son Canaan—were wicked and deserved the harsh punishment they received.

Contemporary readers are more often persuaded by the theory that Ham sexually abused his father. From the perspective of Genesis, they argue, Ham must have engaged in incest. This interpretation is supported by the appearance of the Hebrew idiom “seeing his father’s nakedness” in other biblical contexts. Uncovering nakedness (galah ‘ervat) is a euphemism for illicit sexual activity in Leviticus in particular, where Israelites are instructed not to “uncover the nakedness” of their relatives. Leviticus states:

None of you shall approach anyone near of kin to uncover nakedness: I am the Lord. You shall not uncover the nakedness of your father, which is the nakedness of your mother…You shall not uncover the nakedness of your father’s wife; it is the nakedness of your father… (Leviticus 18:6-8)

In Leviticus, inappropriate sexual activity is identified as “uncovering nakedness.” In one instance, seeing nakedness is also used to describe incest: “If a man takes his sister, a daughter of his father or a daughter of his mother, and sees her nakedness, and she sees his nakedness, it is a disgrace, and they shall be cut off in the sight of their people; he has uncovered his sister’s nakedness.” According to the logic of Leviticus, then, by looking one “uncovers the nakedness” of a body that is designated for someone else: a wife’s nakedness belongs to her husband, a mother’s nakedness belongs to the father not the son, a half-sister’s nakedness is identical to the nakedness of her brother (presumably since brothers and sisters share a parent) and so should not be uncovered, and so on.  Influenced by Leviticus, perhaps readers of Genesis are to imagine that Ham committed incest with Noah, or even raped him. In any case, “seeing nakedness” appears to have sexual overtones.

There is yet another interpretive possibility: perhaps readers are to imagine that Ham engaged in incest not with his father but with his mother. The nakedness of one’s mother is identified as identical to the nakedness of one’s father in Leviticus (“You shall not uncover the nakedness of your father, which is the nakedness of your mother,” Leviticus 18:7). Moreover, in Deuteronomy, incest with a father’s wife is described as “uncovering the father’s skirt.” The nakedness Ham uncovered may have been that of his mother. If so, the curse of Canaan rather than Ham becomes somewhat more logical: Canaan can be understood as Ham’s progeny via his sexual liaison with this mother. Noah then curses the product of their union, just as Yhwh cursed the product of David and Bathsheba’s adultery, leading to the death of their first child.

Whichever interpretation is preferred, however, Ham, the legendary son of the primeval patriarch Noah, is depicted in Genesis as engaging in some sort of shaming sexual infraction. As a result, Genesis suggests, Canaan and his descendants ought to be legitimately enslaved in perpetuity, a claim that would go on to have disastrous consequences when reapplied several centuries later in the context of North American slavery.

Recommended Bibliography:

Aaron, David. “Early Rabbinic Exegesis on Noah’s Son Ham and the So-Called ‘Hamatic Myth.’” Journal of the American Academy of Religion 63.4 (1995): 721-59.

Bergsma, John Seitze and Scott Walker Hahn. “Noah’s Nakedness and the Curse of Canaan (Genesis 9:20-27).” Journal of Biblical Literature 121 (2005): 25-40.

Hayes, Stephan. Noah’s Curse: The Biblical Justification of American Slavery. New York and Oxford: Oxford University Press, 2002.

Johnson, Sylvester A. The Myth of Ham in Nineteenth-Century American Christianity: Race, Heathens, and the People of God. New York: Palgrave Macmillan, 2004.

Koltun-Fromm, Naomi. “Araphat and the Rabbis on Noah’s Righteousness in Light of Jewish-Christian Polemic.” In The Book of Genesis in Jewish and Oriental Exegesis. Edited by Judith Frishman and Lucus van Rompey, 52-72. Leuven: Peeters, 1997.

Steinmetz, Deborah. “Vineyard, Farm and Garden: The Drunkenness of Noah in the Context of Primeval History.” Journal of Biblical Literature 113 (1994): 193-207.