In arcade machines, this is the time in which there are no credits in the machine, and it cycles through several animations and/or demos of the game itself.
For example, in the Mortal Kombat series of arcade games, the attract mode usually consists of several screens detailing the background story of the game, character biographies, and demo fight rounds.
Attract mode is so named, because the combination of sound and flashy animations is designed to "attract" people into playing the game. It also has the added benefit of discouraging screen burn-in.