Yes, the kickback is the result of a switch opening in series with an inductor that is carrying current. Since the current through an inductor cannot change instantaneously when the switch opens, the voltage kickback generated can be quite large (limited only by the parasitic capacitance involved, and arcing breakdown voltages involved). Are you familiar with this differential equation relating the voltage and current for an inductor?
v(t) = L \frac{di(t)}{dt}Some of the details are proprietary to the company that I work for, but I can speak in generalities. Yes, a comm transformer is a communication transformer, used in some communication network. You are probably familiar with Ethernet networks, right? Ethernet network physical connections ("Phy connections") use communication transformers tuned to the frequencies used for whatever bandwidths are needed.
The circuit that drives the "near side" of the comm transformer (the side of the transformer that faces the device, as opposed to the side that connects to the network wiring) has some power supply voltage. It is typically either 5V or 3.3V, although other voltages could be used. When you have a transmit (TX) amplifier circuit, it needs its power supply voltage to be larger than the output waveform that it is driving into the comm transformer. Depending on the type and topology of the TX amp, it can need on the order of 2V of "headroom" outside of the TX signal in order not to distort the signal. So if you have a 2V TX waveform that you want to get through a comm transformer onto the network, and you have a 5V power supply, your TX amp should be okay, since you have 5V-2V=3V of headroom, and you only need 2V of headroom.
But, if the comm transformer has a large leakage inductance, there will be an extra voltage drop across that leakage inductance (Lk) in addition to the voltage drop across the leakage inductance (Lm), and that extra voltage drop erodes your headroom. If the extra voltage drop across the Lk increases the drive voltage into the near side of the comm transformer enough (like by 1V in this example), then you will start running out of headroom in your TX amp, and that will cause distortions in your TX waveform, which can cause comm errors in your network.
Hope that helps some. Ask more questions if things aren't clear yet.