How does adding energy into a system cool it down? (How does air conditioning work)?

Inspired by my previous question, I’ve always been a little curious as to why air conditioning requires so much energy to run.

If I understand A/C correctly, you’re passing air over a super-cool element (say, a tube filled with freon). The energy passes from the air into the freon, heaiting it slightly.

The freon is then pumped into a condenser, which then releases (?) the heat back into the atmosphere, away from your nice cool home or car.

So, is it the case that you’re just transporting the heat to another place where it doesn’t matter, and that’s what requires the energy? Is my understanding of the condenser correct?