A contra dance stage can be a bit chaotic and noisy, especially during a dance. It's a good fit for gestures, and over time callers and musicians have settled on a few covering the main things they need to communicate. I couldn't find a listing of these anywhere, so here are the main ones:
Closed hand facing down with thumb and finger extended, rotate wrist to waggle: change tunes.
A number of fingers: this many more times through the dance after this one.
Lift leg or raise fist: going out at the end of this time through the dance.
Fingers across throat ("cut"): go out immediately, not at the end of the tune or phrase.
Palm facing up, repeatedly lift fingers: play faster.
Palm facing down, repeatedly lower fingers: play slower.
Place hand on the top of the head, palm down: the top of the tune goes now.
The tune change sign is usually advisory, letting the band know that if they want to change at some point they're close to running out of time. If the caller does it early and emphatically, though, it can mean that the music is really not working for the dance and you should play anything else.
Holding up a number of fingers to indicate the number of times remaining is best done in the second half of the tune (B part), to make it clearer that you know you're not counting the current time through.