Compact support

"Compact support" is a fancy way of saying "it only works in a certain area."

Think of your toys, they only work in your room, right? They can't work outside your room, because they were made for your small room only.

Similarly, when you hear about a function having "compact support," it means that it can only work in a certain part of a bigger space. Just like how your toys only work in a certain part of your house.

This is useful in math because sometimes we only care about how a function works in a small part of a bigger space. It helps us solve problems in a simpler way, like when you only play with your toys in your room.