Quotient stack

Imagine you have some toys and you want to share them equally with your friends. But some of the toys are special and you don't want to share them. So you put those special toys in a separate box and only share the other toys with your friends.

The way you shared the toys is like a quotient stack in math. The toys that were shared can be thought of as the "quotient" and the special toys that were kept separate can be thought of as the "stack."

In math, a quotient stack is a way to divide or "quotient" a space by a group action, but keep track of some extra information that is not affected by the group action. This extra information is like the special toys in our example.

For example, let's say you have a circle and you want to divide it into two equal halves. If you just cut the circle in half, you lose some information - you don't know which half was on the left or the right. But if you put a dot in the center of the circle before cutting it, then you can remember which half was on which side of the dot.

In math, the dot is like the extra information that is not affected by the group action. This extra information is important because it can help us understand the space better.