Convergence of random variables means that two random variables get closer and closer together in value as you observe them more and more. For example, let's say you want to know the average number of apples in a single bag. You check the first bag and there's 5 apples. You check the second bag and there's 4 apples. The third bag has 4 apples too. As you look at more and more bags, the average number of apples will get closer and closer to 4, and eventually it will stay around 4. That is an example of convergence of random variables.