Fellows, thanks all your replies, these answers are really helpful.

I agree with what others have said: "cue applaus" means to encourage an audience to start clapping. However, I wanted to add that this is sometimes used sarcastically (as a joke). For example: I show my friend a cake I have baked. It is terrible. I say, "at least the kitchen's not on fire!" My friend pretends to be impressed, even though she is not. She says, "cue the applause."

Generally, if in speech, it means the person speaking has just told you about something they have done that is good. They are pointing out that this is the time to applaud, if perhaps it was in a show. I managed to convince the cafe to stop serving that awful mince at lunch. Cue applause.

During a talk show, if the host wants the audience to applaud (clap at something he just said), a person behind the camera will hold up a sign that says "clap", and the audience will clap. The host just cued applause.