A poker term bad beat applies to hands where a player got their chips into the middle as a big favorite and ended up losing. Technically speaking, any situation where a hand that is a mathematical favorite loses against a few outs is a bad beat, but there are different degrees.
An example of a particularly hard bad beat in Texas Hold’em would be losing with a flopped set against a single pair. For example, you get all-in with a set of 6s against AQ on the board of A-6-5. The turn and the river come running queens to give your opponent a bigger full house.
Every poker player has countless bad beat stories to tell, as these are a natural part of the variance. For the same reason, players don’t like hearing about other players’ bad beats unless they are truly spectacular (like losing with quads to a straight flush).