What are the advantages of an ESC over a PWM?
A BLDC motor is a 3-phase AC motor, which is why there are three wires. 

An ESC is a set of 3 half-bridges that drive the motor phases to create a rotating magnetic field. Below is a schematic from here that should give you some idea. 



If you were to feed PWM to two wires of a BLDC motor it would do very little except get hot and stay in one place. 

Ideally, the output would like this (the frequency is varied to change the motor RPM, 60Hz is shown).. image borrowed from here.  



A video showing what the non-ideal waveforms look like is here: