it does not need to be on a system. it is used to play flash files, some games, ads, videos, toons. one of the first things i download is macromedia flash, because i watch flash toons often.
Flash is an interactive, dynamic Media. Flash Player is the software that allows your browser to play the files. If you have ever gone to a site and there is sound and things are moving, chances are it is probably flash.
To be more specific, Flash technology is a type of dynamic animation compression, which operates from the browser similarly to audio files, avi's, and other plug-in run web technologies. Just like you have to have the QuickTime plugin to watch quicktime movies, the same goes for Flash content.