Definition of crying call
An crying call is often a call that is made on the river. It can also be done at the flop when a player is all in. An crying call is a call that is made by thinking that it is probably mathematically a winner, even though we don't often have the best hand at caller. We have the calls that we do was very happy with it, for example with the nuts on the river, we have the fold clear to do and we have the games halfway between the two. The crying call is never easy. We could translate it as "a call crying".
Some more information about the crying call
To sum up, when you make an crying call, it's like saying: "I probably don't have the best hand, but mathematically it's a caller winner, I have no choice". You can also crying call in a situation where you have (for example) the best hand about 10% of the time, but given the size of the pot, you don't have a choice of caller. For example, on the river, one player bets, you have the flush to the ace and you raise big. On the other hand, your opponent pushes all in. The board is paired and that player doesn't bluff much. Presumably, he has a full hand. You won't often get the best hand, but the pot is too big to fold, so you make an crying call.