There are various different types of chess problem:
Directmates - white to move first and checkmate black within a specified number of moves against any defence. These are often referred to as "mate in n", where n is the number of moves within which mate must be delivered. In composing and solving competitions, directmates are further broken down into three classes:
Two-movers - white to move and checkmate black in two moves against any defence

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Godfrey Heathcote, Hampstead and Highgate Express, 1905-06 (1st Prize): White to move and mate in two. (See solution)