Flash is a piece of shit software, purchased by Adobe, that can be programmed to display many types of scripted media such as games, advertisements, website elements (or, as some morons do, entire websites) and video files.
The most important feature of Flash is its ability to be used to create games. Flash games can be very fun time wasters. Along the same idea of a game, Flash can be used to make animations. A classic example of Flash animations would be the ones created by Xenon.
A Flash loop is a Flash animation that continuously loops. It is usually used for short animations that seamlessly repeat.