For example:

Player 1 holds AA
Player 2 holds KK

The community cards are: AAKKQ

Player 2 would have four of a kind, Kings but still lose to Player 1 who holds four of a kind, Aces.

This is usually enough to trigger a bad beat jackpot for the hand. Normally the losing player in this hand would be awarded 50% of the jackpot fund, the winner gets 25% and other players who took part in the hand get the remaining 25%. Different poker rooms offer different levels of payouts for bad beat jackpots and have different losing hand requirements, for example, Party Poker bad beat jackpot winners must lose with a hand of four 8s or better to qualify.