1. Describes an application which requires a program to respond to stimuli within some small upper limit of response time (typically milli- or microseconds).
Process control at a chemical plant is the classic example.
Such applications often require special operating systems (because everything else must take a back seat to response time) and speed-tuned hardware.
2. In jargon, refers to doing something while people are watching or waiting.
"I asked her how to find the calling procedure's program counter on the stack and she came up with an algorithm in real time."
Used to describe a system that must guarantee a response to an external event within a given time.