Okay kiddo, imagine you have a toy car that you don't really want anymore but you really want a toy truck instead. Let's say your friend has a toy truck but they really want a toy car instead. Instead of you and your friend having to spend a bunch of money on brand new toys, you can make a deal to swap toys with each other.
This is kind of like what part exchange is for grown-ups. When someone wants to buy a new car from a dealership, they may not want to keep their old car anymore. Instead of selling it independently or trying to find someone who wants to buy it, the dealership might offer to take the old car as part of the payment for the new car. They’ll give the person some money for the old car, and put that towards the price of the new one. This means the person doesn't have to worry about trying to sell their old car somewhere else.
So, part exchange is basically like a big toy swap, but for grown-up stuff like cars!