White promotes to a Queen because it is the easiest of the Basic Mates. A Rook would also win, but not a Bishop or a Knight. You can't get checkmate with these because they can only control one colour of square at a time.

Straight away, the new White Queen begins to take squares from Black's king.

Now it is Black's move. When there are very few pieces on the board,
a lone king can survive for longer if he is in the middle. Black's best move is to play Ke5. Click on the Black king to watch him move there.