Any pair that is lower than the highest card on the board (especially those that are lower than all the cards on the board). If you hold 33 and the board is showing KJ6, you have an underpair. See also: Overpair.
A pocket pair of lower value than the lowest card on the board.
A pocket pair underneath the lowest card on the board. E.g. You have 66 and the flop is Ac-9h-Th. You have an underpair to the board.