If White has to move then he gives a checkmate at a7, b7, c8 or d8. (1.Qa7++ or 1.Qb7++ or 1.Qc8++ or 1.Qd8++ Learn Chess Notation)
If Black has to move then he cannot make a legal move so it is a stalemate. This means nobody wins, it is a draw and half a point each. 0.5/0.5
Black must move the king as he has no other pieces left. But the black king is not allowed to go to b8 because this square is protected (covered) by the queen. The black king is not allowed to go to a7 or b7 because these squares are protected (covered) by the white king AND the white queen. All this means Black is unable to make a legal move and this again means it is a Stalemate (draw, half a point for each player).
If you are a queen up in material then make sure that the king of your opponent has always a square where he can move to until you finally checkmate him. This avoids a stalemate.
You should win when you are a queen up. It is simply embarassing when you can't win and achieve a draw only while being a queen up.