HUD is short for Heads Up Display and is a function of programs called trackers. A tracker collect hand histories from all the hands, you played at a
poker site, which allow you to look at them later and analyse your game.
If it is allowed by the poker site, you can also choose to enable the HUD. As others have explained, the HUD will show in real time statistics about, how your opponents have played in previous hands, where you were sitting at the same table as them.
Basically this is usefull for making adjustments. If you notice, that someone has hardly been playing a hand for the last hour, but now he suddenly go all in preflop or on the flop, then you can safely assume, he have something very good, so unless you have the nuts, you can pretty much just fold and not pay him off.
If on the other hand he has been all in preflop or on the flop 5 times in the last 14 hands, you can assume, he is a wild player, who is just splashing his chips around. So if he goes all in on the flop again, and you have something pretty good but not nutted like top pair good kicker, maybe this is the time to give him action and hope for the best.
This is a very simple example, and for the wild guy, you dont really need a HUD. You just need two eyes to observe, what he is doing. But the other guy, the nit, can be more difficult to spot, especially if you play multible tables, and this is where, the tracker and HUD is helpful.