I have a 11hp rear engine snapper. The motor shut down on me so I took it off and replaced with a 12.5hp. The only 2 wires the 11hp had was a starter wire and another that went inside the lid. This 12.5hp has those 2 wires plus 2 more that are both coming out of the side together in the same connector. Both are male ends that female ends connect to. Does anyone know what these wires are for?

11 sounds like its pretty old? Then that wire was probably the wire from the alternator, to the battery to charge it (runs lights, etc).
12.5 sounds like it has a power wire (for battery) with diode (should be a single wire?) and 2 wires for lights...
This should help you. http://www.tulsaenginewarehouse.com/.../allwiring.pdf