ESD protection on 10/100/1000 ethernet
Check the datasheet for Rclamp3374N. It has a common GND connection that is the dissipation point for the ESD strike (GND goes to the big diode in the middle, to the anode side.)
The Rclamp3374N clamping action limits the signals to between GND and the Zener breakdown voltage of about 3.5V. Ethernet signals are smaller than that (+/-2.5V differential) so normally the TVS doesn't conduct in the presence of Ethernet PHY signals alone.
Why use the ESD array then, and why on the PHY side? The magnetics do a good job of isolating spikes induced onto the field wiring, using both built-in common-mode filters and galvanic isolation between the wires and the PHY. But these magnetics are not perfect: some ESD energy can still shoot through the transformer due to mutual coupling and capacitance.
The ESD array catches this residual energy before it can make its way the PHY: it's a last line of defense. This will improve your ESD/EMC testing performance and make your product more robust in the field.
Could you use ESD protection on the field wiring side? Sure, it's possible. Generally though no assumption is made about the wires' common-mode voltage with respect to the system, which complicates designing a spike catcher for them. Further, the magnetics are deliberately designed to maximize the system-to-wire isolation as much as possible, with the exception of the 'Bob Smith' termination; a wire-side ESD array would partially defeat that.
Finally, note that the Rclamp3374N package is laid out in such a way that the PHY signals route through it to reduce impedance discontinuities. Make sure you take advantage of that when you lay out your board.