It means getting a decisive advantage. In chess circles and literature, three levels of advantage are commonly used: slight advantage, clear advantage and decisive advantage. The latter is when it becomes irreversible so the win should be secured not matter what as long as you keep playing well. For example, a significant material advantage such as two extra pawns, an extra piece, etc. is usually decisive. The other levels of advantage can increase to a decisive level or decrease to equality. So, when my puzzle instructions say: "White to play and win" it means finding the path to the decisive advantage.