Another fun stage direction term. This refers to the prompt corner, a spot (usually a desk of some sort) from which the stage manager can communicate with the actors and crew. Traditionally the prompt corner is on stage left, that is, left as you stand on stage and look out at the audiance.
So 'prompt side' is another name for stage left. It is often refered to as PS, or just prompt. The opposite of prompt side is opposite prompt or off prompt, in either case often shortened to OP.
Prompt side is always stage left, even if you have a bastard prompt, i.e., a prompt that is on stage right.