One-armed bandit is a long-standing nickname for a slot machine. The "arm" is the side lever early machines used to set the reels spinning, and "bandit" refers to the fact that, over time, the machine keeps more than it pays out.
Mechanical machines from the Liberty Bell era onwards used the lever to wind the mechanism. Later electromechanical and electronic machines kept a lever for familiarity, though a button did the real work; most modern machines and all online slots use a button only.
The name is a fair summary of the economics. Every slot has a house edge, and the bandit always wins in the long run. See our history page.