What’s the deal with “tags”?

This may sound like a stupid post but hey, I’m not getting the hang of it!

Every now and then I run into phrases like “popular tags” and the like on blogs. I know what a tag is here at the support forum, but when a lot of WP bloggers are using them I’m beginning to wonder if it is some sort of plugin for tagging posts for indexing beyond the categories?

Could someone fill me in? Thanks.