What does Genesis 7:7 mean?

Only eight people will survive the flood, which will otherwise wipe out all of humanity. Noah and his wife and their three sons and their wives would shortly become the only people left on the entire planet. This is a common point held between those who interpret these verses as a local flood, and those who see a global flood. Whether these waters covered the entire surface of the globe, or only the regions inhabited by man, the purpose and effect is the same.

In the prior chapter, God saw that the human race was spiraling out of control. Everything was poisoned by evil (Genesis 6:5), and everything man did was abusive and vile (Genesis 6:11–12). The only exception, it seems, was Noah (Genesis 6:9). Rather than allow mankind to fall into complete ruin, God chooses to judge evil. And, in doing so, to spare those who honor Him. In this way, the human race can survive, but his drastic turn towards evil can be stopped.

Noah's three sons, Shem, Ham, and Japheth were each around 100 years old at this time, still relatively young men by the lifespans of their era.