What is so important about the time “11,000 BC” and “13,000 years ago,” which come up frequently in this chapter of Guns, Germs, and Steel?
I assume that you are asking about Chapter 1 in the book. If so, the reason that this time is so important is that it was the time at which agriculture was first developed. The development of agriculture (also called food production) is hugely important for Diamond. Diamond argues that the areas that developed food production first were the ones that had a huge advantage in becoming powerful societies. This is his basic answer to Yali's question--that areas that had geographic luck developed farming first. Because of farming, these areas came to have the "guns, germs, and steel" that made them powerful and prosperous.