What is a third-party purchase?

In layman's terms, a purchase that is made by a "third party" or "third person" is when the buyer is someone other than the one it is intended for. In other Words, Jack wants to buy a pail of water from Jill, but he has no money. So Jacks' mother buys the pail of water for Jack. Jack's mother is the "third party" or "third person" who is making the purchase.