Most of the animated cartoons seen online or received in an email are called gifs, because of the ".gif" (Graphic Interchange Format) extension appended to their file names. An "animated gif" is a series of pictures in which each successive image has something move slightly from its previous position (similar to a traditional movie film). When a complete strip is viewed on your monitor, the succession of images will give the illusion of, say, a leprechaun doing a jig.
It's important to understand that gifs are not the same as more sophisticated animations, such as those created with Adobe Flash. Gifs can be easily copied and pasted, while Flash movies cannot.
Photo courtesy of Toolson.net