The way it likely works is 12 volts is applied to the board from the battery, U3 supplies 5 volts to the pic processor. when the switch/pot is activated the pic outputs a pwm signal to Q4 & Q5 then to the output transistors (this is the variable speed signal) then the pic also turns on the relay connecting the transistor output to the motor, driving the motor at whetever the speed pot is set to. The relay is likely also used to provide dynamic braking for the motor
Q7 looks like the relay drive transistor, D3 is protection across the relay coil.
I believe that diode D1? (to220 dual diode?) is likely connected across the motor to protect the output transistors.
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