What does Genesis 6:10 mean?

Noah's three sons are listed again, as they were in Genesis 5:32. Along with Noah and his wife, these men and their wives will be the only humans saved from God's judgment on the sins of humanity. Few other details are given of their lives or character. Strictly speaking, we don't know who was the oldest or youngest, or exactly how old Noah was when they were born. Genesis 5:32 gives a rough idea of Noah's age, but has every appearance of a general statement, not a specific one. Though the Bible does not say so in explicit terms, we might assume that Noah's sons also stood apart from the normal wickedness of humanity (Genesis 6:5, 8). This is mostly because they are welcomed on the ark.

The other patriarchs of Genesis chapter 5 are credited with having "many" sons and daughters. Noah is not described in this way. While the Bible does not say, directly, that these were his only three children, that is certainly likely. Noah's father Lamech died prior to the flood, and the three sons mentioned in this chapter all survive with Noah on the ark. It's possible that this was all part of God's favor on Noah: limiting the loss of his family in judgment.

Another, sadder, possibility is that Noah had other children, who are not mentioned in the Bible. The other patriarchs of Genesis chapter 5 are credited with having children at a much younger age than Noah's 500 years at the birth of these three sons. It's not impossible to think he might have had other children before Shem, Ham, and Japheth. If so, those other offspring would have been destroyed along with the rest of the evil world in the flood.