An on-screen super (short for superimposition) is a particular type of television graphic that has become extremely prominent in the last few years due to advances made in computer technology - basically, whenever you see a image on-screen that doesn't actually exist in the world of the television program you're watching, that's an on-screen super.
The earliest supers were the network logos you can see in the corners of your television screen during, well, practically any show you'll find on-air. Sometimes they appear after commercial pods and sometimes they last the length of a segment, but they're usually there - it's a way of keeping the channel surfers informed of where they are in the spectrum and is a good way of keeping brand recognition high among people who settle on your network but don't stay long enough to hit a commerical break.
Recently they've gotten far more complicated and, some would say, intrusive. Rather than merely sitting pretty in the corner, supers now portray all sorts of information, be they throws to other shows on the network (or, sometimes, as throws to programming on a completely different network, though usually a subsidiary - you'll sometimes see supers for shows airing on USA or Sci-Fi on NBC because NBC owns both of those other networks) or contest entry information and the like. They rarely exist as actual advertisements for products because studies have shown that people would react to such ads with outright contempt. The one (recent) example where this isn't the case are ads for the iTunes Music Store - these supers explain that they show running under it is available for purchase at the iTunes Music Store, and people actually like to know that. If they were hocking detergent, though, the reaction would be quite different.
It's worth noting that supers aren't always advertisements and they certainly aren't always intrusive, though that last point is generally only true of sports programming - the score of an NBA game is a super, as is a reporter's name in the local news, as is...well, you get the idea. It's therefore slightly ironic that such useful supers are being sold to the highest bidder, giving rise to things like the "Taco Bell Running Order" and the "Built Ford Tough Halftime Report" and the like.
The primary difference between a super and a plain-old generated image is that supers always occur on top of actual show content instead of interrupting it.