Flash enables some kinds of web animations and video delivery. It is most commonly used for games, ads, videos, ads, web cartoons, ads and more ads.
I consider it useful to have for some websites that are very dependent on it, but it's equally important to block it as it is the number one source of security issues and instability on web browsers (don't take my word for it, ask Google and their Chrome team).
There's an extension or plug-in for most web browsers called ClickToFlash that disables Flash (though it can "whitelist" certain sites) and allows you to re-enable it on a case-by-case basis.
I personally prefer to use AdBlock (again I can whitelist some sites, like Mac sites, since I probably AM interested in their ads) along with a flash-video-to-HTML5 converter rather than ClickToFlash, but the latter is very good at what it does and with a little training lets the "right" Flash in and keeps the annoying Flash out. For me, however, the former combo does more-or-less this job with less input from me.