They Propose their post as an answer (blue check). Only the original poster (OP) can Mark a post as the answer (green check).
Personally I think that Propose as answer is a very bad feature. The only people who use it are generally either the responder (arrogant) or the OP (usually an error based on misunderstanding).
Occasionally, a third party will use Propose as answer, but the only time it happened to one of my replies, my response did not actually work for the OP, so it was not the answer he was looking for.
I suggest getting rid of Propose as answer, because I believe it serves no useful purpose.