A crying call is a call made on the river in a situation where a player does not think they are likely to win, but believes there is some small chance they may win. The term comes from the notion that the player would be crying as they call, since they are sad that they are nearly certain to lose.
A crying call is most often associated with fixed-limit games, where the ratio of pot size to bet size can be quite large. Nevertheless, a well-sized (read: strategically small) value bet in big bet games can also induce a crying call from a hand unlikely to be best. ("I only have to call another $10 to see if she really has me beat... oh, ok.")