Why does this DC motor controller use relays and also MOSFETs?
Briefly connecting both motors to the same terminal (either works, yours chose positive) shorts out the motor. This brakes it, which reduces current surges while reversing.
What the MOSFET is for is anybody's guess, unless you know what is driving the gate. It could provide soft starting, or an electronic disconnect in the event of overload, overheating, etc.