There is a little story about Noah that takes place a short time after the Ark was landed. It is an odd story, and without a wider context, can be very perplexing.
From what the story says, Noah got drunk, and his son, Ham, found him in his tent naked. So Ham came out and told his brothers, who backed into the tent and covered him with a garment. Then when Noah woke, he cursed Canaan.
It sounds a little odd, I know, but the Church’s Institute Student Manual has an interesting explanation. I’ll paste it after the verses. Basically, Noah got drunk in his tent and passed out (remember the word of wisdom was not revealed until this dispensation). Then Ham, who held the priesthood, but who’s son could not hold the priesthood, thought that he could give his son the priesthood by giving him Noah’s garment, so he stole it off his father. When Shem and Japeth discovered what had happened, they made him a new garment and put it on their father. So when Noah woke, he realized what happened and cursed Canaan, who had the stolen garment.
Here’s the account:
20 And Noah began to be an husbandman, and he planted a vineyard:
21 And he drank of the wine, and was drunken; and he was uncovered within his tent.
22 And Ham, the father of Canaan, saw the nakedness of his father, and told his two brethren without.
23 And Shem and Japheth took a garment, and laid it upon both their shoulders, and went backward, and covered the nakedness of their father; and their faces were backward, and they saw not their father’s nakedness.
24 And Noah awoke from his wine, and knew what his younger son had done unto him.
25 And he said, Cursed be Canaan; a servant of servants shall he be unto his brethren.
26 And he said, Blessed be the Lord God of Shem; and Canaan shall be his servant.
27 God shall enlarge Japheth, and he shall dwell in the tents of Shem; and Canaan shall be his servant.
And here’s the explanation given in the Institute Student Manual:
(4-20) Genesis 9:20–27 . Why Did Noah Curse Canaan in This Event When He Was Not Even Present?
The account of Noah’s “nakedness” and the role his sons played in the event is a puzzling one, especially the part in which Noah awakens and pronounces a curse upon Canaan, the son of Ham (see Genesis 10:6 ), who does not even seem to be present at the time.
Most members of the Church are aware that a priesthood garment, symbolic of the covenants made in the temple, is worn by those who have participated in the endowment ceremony in the temple. This garment is a representation of the coat of skins made by the Lord for Adam and Eve after the Fall (see Genesis 3:21 ; Moses 4:27 ). The idea of a garment made of skins that signified that one had power in the priesthood is found in several ancient writings. Hugh Nibley discussed some of these ancient writings and their implications for the passage in Genesis:
“Nimrod claimed his kingship on the ground of victory over his enemies [see Genesis 10:8–10 ; Reading 4-21 ]; his priesthood, however, he claimed by virtue of possessing ‘the garment of Adam.’ The Talmud assures us that it was by virtue of owning this garment that Nimrod was able to claim power to rule over the whole earth, and that he sat in his tower while men came and worshiped him. The Apocryphal writers, Jewish and Christian, have a good deal to say about this garment. To quote one of them: ‘the garments of skin which God made for Adam and his wife when they went out of the garden and were given after the death of Adam . . . to Enoch’; hence they passed to Methuselah, and then to Noah, from whom Ham stole them as the people were leaving the ark. Ham’s grandson Nimrod obtained them from his father Cush. As for the legitimate inheritance of this clothing, a very old fragment recently discovered says that Michael ‘disrobed Enoch of his earthly garments, and put on him his angelic clothing,’ taking him into the presence of God. . . .
“Incidentally the story of the stolen garment as told by the rabbis, including the great Eleazer, calls for an entirely different rendering of the strange story in Genesis  from the version in our King James Bible. They seemed to think that the ’erwath of Genesis [9:22] did not mean ‘nakedness’ at all, but should be given its primary root meaning of ‘skin covering.’ Read thus, we are to understand that Ham took the garment of his father while he was sleeping and showed it to his brethren, Shem and Japheth, who took a pattern or copy of it (salmah) or else a woven garment like it (simlah) which they put upon their own shoulders, returning the skin garment to their father. Upon awaking, Noah recognized the priesthood of two sons but cursed the son who tried to rob him of his garment.” ( Lehi in the Desert and the World of Jaredites, pp. 160–62.)
Therefore, although Ham himself had the right to the priesthood, Canaan, his son, did not. Ham had married Egyptus, a descendant of Cain ( Abraham 1:21–24 ), and so his sons were denied the priesthood.