The attract mode is an almost universal concept among arcade games. Even the manual to my 1975 Shark JAWS machine goes into great detail about how the shark swims around when no one is playing. The basic idea is that the attract mode is supposed to "attract" people to the machine.
Your most basic attract mode will just be the game playing itself over and over again, usually going through the same 30 or 40 second sequence each time. More advanced attract modes can go for as long as twenty minutes or so without repeating themselves.
The best attract modes are the ones that actually tell you how to play the game. For example, the Robotron 2084 attract mode goes through all the enemies and game options step by step without missing anything.
Most games (unfortunately) make noise during their attract modes. This may not matter in a crowded arcade setting, but it can get quite annoying listening to the Teenage Mutant Ninja Turtles theme song every 2 minutes when you are at home. Fortunately you can usually turn off attract mode sound in either the setup menu, or with a dip switch setting. But some games still insist on making the occasional sound. For example, Star Wars will still play the cantina music about once every 30 minutes, and Galaga will make a few shooting sounds every once in a while (I have been woken up by those noises more times than I can count).
The late eighties brought about public service messages in the attract modes of many games. Who can forget the "Winners Don't Use Drugs" screen that so many games prominently displayed. Some games will even sell products, as Mortal Kombat hyped it's comic book for sale. The ad could be disabled with a dip switch once the offer expired.
Finally, many games allow you to enter a custom message that will be displayed in attract mode. Check your manual, you might very well be able to advertise that this is "TBBK's Joust Machine", or you could even be clever and have it say "Candace will you marry me?" (let me know if that one works out).