The "widebody revolution" started in the late 80's with models such as the Wilson Profile. Different companies have produced various rackets that vary in their widebody construction .
Generally, Wider - More powerful, stiffer, more expensive. Widebodies are usually 18mm (very narrow) up to 30mm wide. The general rule of thumb is that the quicker and longer a stroke motion you have, the narrower a racket you should use (not a hard-and-fast rule, though).
It should be noted that you are not going to find non-widebodies around. Almost every racket is wide to some extent. One problem with widebodies occurs when people try to hit the ball edge on as in extreme sliced shots or topspin shots. You tend to hit the side of the racquet a lot more. You can compensate through a bit of practice.