They're kind of like a scaled-down version of adventure games, where you have to use only the items in the room to accomplish a mission - escaping from a closet, a bedroom, a phone booth, a prison... whatever kind of room or building you are trapped in. You search the area for items you collect, some of which are clues, some of which are combined with other items to aid in your escape. You don't usually die in these games, unless you're racing against the clock. There is one room with a time bomb you have to diffuse.
I love those games, and I play them all the time on sites like http://www.addictinggames.com or http://www.newgrounds.com/game/adventuregames.html.
Some of the games I recommend are:
Escape the Room: http://www.newgrounds.com/portal/view/215251
Escape Elm Street: http://www.newgrounds.com/portal/view/81945
Escape Prison: http://www.newgrounds.com/portal/view/354319
Escape the Phone Booth: http://www.addictinggames.com/escapethephonebooth.html
Trapped: http://www.addictinggames.com/trapped.html
Submachine 1 The Basement: http://www.addictinggames.com/submachine1thebasement.html
Covert Front: http://www.addictinggames.com/covertfront.html
Covert Front 2: http://www.addictinggames.com/covertfront2.html
Intruder (this one is scary): http://www.addictinggames.com/intruder.html
Exmortis (this one is also scary): http://www.newgrounds.com/portal/view/189227 This one has a few sequels you can reach through this game. Exmortis 2 is even creepier than this one.
If you have played these games before, what ones do you recommend? I'm always on the lookout for a cool "escape" game. I do have a hard time finishing during breaktime at work, though.

If have never played an escape game - check some of these out. They're pretty cool, especially for a free game. If I knew how to do simple animation and programming, I would write a ton of these, because I think I could come up with some good ideas.
Enjoy. 8)