After the Flood of Noah, the Bible shows Noah getting drunk and becoming naked in his tent, and his son Ham saw it, and wanted to show his brothers. After Noah was sober he found out what his son had done,

So Noah awoke from his wine, and knew what his younger son had done to him. Then he said:

“Cursed be Canaan;
A servant of servants
He shall be to his brethren.”

And he said:

“Blessed be the Lord,
The God of Shem,
And may Canaan be his servant.
May God enlarge Japheth,
And may he dwell in the tents of Shem;
And may Canaan be his servant.”
(Genesis 9.24–27)

What was Ham’s sin? (See also Habakkuk 2.15.) It was not merely that he saw his father naked, something which may have happened accidentally, but it must have been that he thought it comical and wanted his brothers to see the spectacle Noah had made of himself. Moreover, by observing what the brothers did in response, Ham should have covered his father.

Shem and Japheth saved their father from further embarrassment.

Therefore, Canaan became a servant of the others. Ham had humiliated his father Noah; why then did Noah say: “Cursed be Canaan”? One commentator says,

“That the curse fell on Canaan, youngest son of the offender (10.6), who was himself a youngest son, emphasizes its reference to Ham’s succession rather than his person. For his breach of the family, his own family would falter. Since it confines the curse to this one branch within the Hamites, those who reckon the Hamitic peoples in general to be doomed to inferiority have therefore misread the Old Testament as well as the New. It is likely, too, that the subjugation of the Canaanites to Israel fulfilled the oracle sufficiently (cf. Jos. 9:23; 1 Ki. 9:21)” (Kidner).

Also in verses 18 and 22 it is said that Ham is the father of Canaan. Why is this mentioned? Ham had four sons total (10.6), and Canaan was the youngest. It might be that the mentioning of Canaan in this narrative shows that he had a part in this sin. Warren Wilcox has the following comments,

“Noah’s curse is not one that says ‘cursed be Canaan,’ but rather, ‘cursed is Canaan.’ It also says, ‘a servant of servants shall he be,’ not ‘may he be.’ Leupold indicates this is a better rendering since the construction is not in the optative sense. Therefore, God is foretelling the future, not determining it. To foretell that Canaan’s descendants will display a moral impurity to the point they must be condemned by God involves no injustice on his part. He did not make them become evil; he merely foretold the curse of slavery upon them because, as history reveals, they became so evil…” (Difficult Texts of the Old Testament Explained, p. 223).