Help Identify Potential BLDC Protection Circuit
The main thing this circuit does is protect against reverse polarity from an improperly-connected battery.

The inductor and capacitors provide noise suppression.

The reverse-polarity protection is a trick I first saw described by Bob Pease {National Semiconductor}. 

If you look at the current flow through the MOSFET while the battery is connected properly, you will see that the reverse-connected diode inside the MOSFET is forward-biased. That would normally result in a voltage drop of about 0.6 Vdc. However, the Gate has a positive voltage with respect to the Source. The MOSFET is thus fully-enhanced, resulting in a very-low voltage drop. 

If the battery is reverse-connrcted, the internal diode is reverse-biased and the Gate is also reverse-biased. The MOSFET does not conduct and thus protects the rest of the system.