Only the person who asked a question can select a best answer. We do this inside our own account, under Q&A, My Question Statistics. In the Best column, pick Choose. Scroll down to the answer you think is best, and choose "Select as Best Answer." This cannot be undone.
I think perhaps you misunderstood the question that confused you. I believe the person who wrote it was assuming that the chooser was the person who asked the question in saying "chooses the best answer to their question." That is, the person asked the question, it is theirs. Some people who ask a question also choose a best answer to their own question. I hope this helps.