MOSFET Circuit To Alternate Polarity
This is probably used to discharge any capactitance that might be connected to the output. Imagine, that You have a capacitor in the led strip (or some other load), and it is not discharged to 0V. Then You switch the polarity and for the moment, capacitor charged with negative voltage is connected to 12V PSU. Q2 is turned on probably just before changing polarity (for some time, due to lack of current sensing through it).