In poker terms, a bad beat is a good hand that got beat by an even better hand. Needless to say, good hands lose all the time, but generally a bad beat would be a full house losing to a better full house, or a four of a kind, etc.
Here's an example for Texas Hold 'em. I hold pocket rockets, the flop shows ace, ten, nine. I bet strong because I just made a three of a kind. My opponent calls. Fourth street shows another ten. I bet again, I have aces full of tens now, an excellent hand. Here comes the river, a three. No help to me, but I bet again because of the strength of my hand. My opponent calls. He shows a pair of tens in the hole and he made a four of a kind using the community cards, and wins. Now that is a bad beat.
Quite a few card clubs also have progressive bad beat jackpots. In order to win the jackpot in the club I've been to, you have to have aces full of tens or better and get beat. The other stipulation is that you have to use both your hole cards, assuming the game is Texas Hold 'em. The nice thing about these jackpots is that the person who got the bad beat takes 50% of the jackpot, the winner takes 25%, and everyone else who played that hand at the table splits the remaining 25%, also known as the table share. I think that is a pretty common breakdown of the winnings at most clubs as well.