simple explanation: your normals are messed up.

Complex - now, the real problem is what you want the thing to look like. if its supposed to be all hard edged, the fix is simple. select the object, click through "Edit Polygons -> [edit] Normals -> Soften/Harden" (I don't have maya open, so I'm a little unsure of the exact titles, but its something like that). Depending on what you have your defaults set to for that command, the look may or may not change, but either way a new node shode have been created - 'polySoften' or somesuch. Click in there, and there should be a number between 0 and 180. 180 is smooth and rounded, 0 is hard and sharp edged. Change as desired.

You can also use this command to modify individual faces, edges, and vertices. Keep in mind, though, that you're almost always going to want to do your smooth normals before your hardened ones (because of the way things seem to flow with them). Anyways, experiment!