The promotion of a pawn having reached the 8th rank to a piece other than a Queen. This type of promotion is sometimes also called as "minor promotion". The most common underpromotion, if happening, is the promotion to a Knight (often with check) to continue a combination. The other choices for it (to a Rook or Bishop) could be considered to avoid stalemate.
Underpromotion is directly connected to the characteristics of the given position. It is highly recommended to do a thorough analysis of the position to identify the important details helping you make the right decision.
A well-known underpromotion occurred in the game Korody-Balogh, Budapest 1933:
1.d4 d5 2.c4 e5 3.dxe5 d4 4.e3 Bb4+ 5.Bd2 dxe3! 6.Bxb4 exf2+ 7.Ke2 fxg1N+ 8.Rxg1 Bg4+ and White resigned.