haha ok, so there is not actually a point to the button and turning around. I figured maybe it meant you won or something.
EDIT: Oh, ok, thanks you all for better explaining it.
There absolutely is a reason
They start facing the other way so they judge the people based ONLY on their voice. While the contestant is singing all four judges have the time to listen closely to the performance. If a judge is interested in having that person join their team, that is when they turn their chair around.
At the end of the song, the contestant can then pick from the four judges who turned around to face them to decide which team they join. If none of the judges turn around, the contestant is automatically off the show. If only one judge turns around, the contestant instantly joins that team and they have no decision to make. Also, again, if more than one judge turns around, the contestant can then pick which team to join.