Offensively you get "an extra man" b/c the defense has to account for the QB as a wideout.
Let's say you've got 2 WRs, 2 RBs, 1 TE and the QB when you go Wildcat. Defensively you have to account for the 3 players spread wide (2 WRS and QB) so that takes away at least 3 defenders, but more than likely 4, as far as being "in the box" or close to the LOS to stop the run. Therefore you are left with 7 defenders and the offense has 5 OL, 1 TE, and 1 RB to block you. So you have 7 players to block vs 7 defenders, this is an advantage for the offense. Yeah, you still have those other 4 guys that are defending against the pass (you have to stay sound defensively), but they are going to make play down the field if you get everyone blocked.
Granted, you can create these advantages by formation, with motions, etc. with the QB in the backfield, but the Wildcat allows you to do this fairly easy and quickly in certain situations.