This term dates back to before there was television and before there were movies but they still do it. When an actor is doing something on stage other than crossing or actions specifically put into the script in order to add believability and realism to their character, they are performing stage business. It's usually simple things that we take for granted as real people. Like playing with the phone cord while pretending to talk on the phone, or doodling on a pad while taking notes as their character questions a suspect; provided it's a murder mystery. Or they could be flipping a coin or playing with their hair. There's no end of possibilities.

The Picard Maneuver is an example of stage business as performed on Star Trek: The Next Generation.

Stage business is the combined small movements and actions that an actor uses to help build information for the audience. If someone is nervous, having someone sit there and say they're nervous is not convincing. Having an actor fidget and look around nervously, however, shows rather than tells the audience that the character is nervous.

An example of this can be seen in scene eight of A Streetcar Named Desire. When Stanley blows up at Stella, we find that he is a crude, abusive man. Some of the stage business that Tennessee Williams scripted (throwing a plate on the floor, roughly grabbing Stella by the arm) shows the audience this, rather than having Stella just saying so outright. This builds in realism, which in turn draws the audience into the story.

Stage business tends to be the one thing missing from high school plays. Most of the ones I have seen had half of the characters just hanging out spouting lines. If I had my druthers, that would be one area I would focus on should I ever find myself behind the director's chair.