Can someone please explain in plain, layman's terms English what FeedBurner does and is? (www.feedburner.com)

It exports your site’s RSS feed to a different server from which you can see stats over how many reads your RSS.

Also if you add feedburner adds to your rss feed you get money for ad views. Along with making money through feedburner you also gain exposure for your feed through their site.

(Assuming you know what RSS feeds are)

Basically, it mirrors your RSS feeds. Badly designed feed readers can put quite a heavy load on your website that you’d have to deal with – by letting FeedBurner copy your RSS feed and having people subscribe to that, FeedBurner can take care of hosting issues.

On top of that, it’s in a position that it can provide some interesting features for your feeds, such as the possibility to track statistics of how your feeds are read, an easy interface for people to subscribe, and more.