Ok kiddo, so imagine you have a really big number, like a gazillion. Now imagine trying to figure out all the different ways you can multiply smaller numbers together to get that big number. That's called factorization!
So, integer factorization records are kind of like a competition to see who can do this the fastest and with the biggest numbers. It's like a race to see who can figure out all the factors of a really really big number first.
Why is this important? Well, some really fancy computer security systems rely on the fact that it's really hard to factorize really big numbers. If someone can figure out the factors of a big number that's being used in a security system, they can break into it and cause lots of trouble.
That's why lots of really smart people are always trying to figure out better and faster ways to factorize big numbers. They keep track of who can factorize the biggest numbers and do it the fastest, kind of like keeping track of who can run the fastest marathon!