The word cue has several meanings:

1. A signal that tells you when to do something. Actors wait for their cue to walk on stage or say their lines. In a play, one actor's last word might be another actor's cue to enter. Musicians watch the conductor for a cue to start playing. When someone says “that's my cue,” they mean it's their signal to act or speak.
2. A long stick used to hit balls in games like pool and billiards. Players hold the thick end of the cue and use the thin end to strike the white ball, sending it rolling across the felt table to knock other balls into pockets. A good pool player can make the cue ball spin, curve, or stop exactly where they want it.
3. To give someone a signal or prompt. A director might cue the lighting technician to dim the lights. Teachers sometimes cue students by making eye contact when it's their turn to present.

The phrase on cue means happening at exactly the right moment, like when you mention rain and it starts pouring right on cue. Don't confuse cue with queue (pronounced the same way), which means a line of people waiting for something.