The Condorcet Criterion is a way to decide which choice is the best one when there are a bunch of different possible choices. Imagine you and your friends are trying to decide what game to play at recess. Someone suggests playing tag, someone else suggests playing kickball, and another person suggests playing four square. The Condorcet Criterion would say that the best choice is the one that would beat every other choice if you compared them one-on-one.
So let's say you and your friends vote and it turns out that tag beats kickball, kickball beats four square, and four square beats tag. None of the choices beat the other two consistently, but tag wins against kickball, kickball wins against four square, and four square wins against tag. So according to the Condorcet Criterion, the best choice would be tag since it beats the other two choices in a one-on-one comparison.