The way I think it works:
You sell the chametz to the goy on loan, so to speak, and the money he gives you initially is collateral (nowhere near as much as the actual value of chametz). After pesach, you “forgive the debt” and give back the collateral for the chametz. It’s pretty much as Ubiquitin explained. The chametz really is the goy’s just like a house really is your’s if you buy it with a loan. If you don’t pay back the loan, the bank takes the house as is probably stipulated in the contract. The same is true here (I think).