<p>Can someone explain the pros and cons of it  and any math involved with it?</p>

It's more accurate than vertexes (or hit-boxes etc). I'm assuming you're talking about 2d here (3d would be box-model vs vertex). Per-pixel would allow you to have detailed sprites which small things (missiles, say) would collide with more realistically.
It's more math and slower than the conventional method, which would be to draw a box (or some other easily math shape like a circle) and say 'this is the actor, anything in here is he'. It is however, more accurate.