Sometimes you count a set in two different ways. If both counts represent the same set, they must be equal. This gives you an equation.
Example: In a group of n people, how many handshakes if everyone shakes hands once? Method 1: Each person shakes n-1 hands, total n(n-1). But this counts each handshake twice. Answer: n(n-1)/2.
Method 2: Choose 2 people from n. Same answer. Both methods count the same thing.