In terms of performance, 3 wire powering can handle much louder SPLs (Sound Pressure Levels) without distorting... you can think of 3-wire powering as a pseudo-phantom powering method.
In terms of the circuit, Audio Technica mics have 3 wires (yellow or white for "audio," red for +9V, and ground wire). The 3-wire circuit keeps all 3 wires "separated" for each microphone.
With a "2 wire" setup--for instance, where you have two Audio Technica mics and they are terminated into one single mini-plug connector--the "audio" (white/yellow) wires and the ground/shield wires are all connected to the sleeve (ground contact) of the mini-plug.