I understand that attaching jumper cables to a car in reverse would damage the battery, but why would it damage the cars electronics. I'm an electrical engineering student in college and if you connected them properly or improperly, the only thing that would change would be the direction of electrical current. So I can see why that would be bad for the battery but why would the electronics get fried?
I'm no engineer or professor so I can't give you exact details but the basic idea is because the modules are only designed to handle a certain current and voltage in one direction. When hooked up backwards the reverse breakdown voltage on many of the components (like polarized capacitors and diodes) will be exceeded and they will short and burn up.
As an Electrical Engineering student I'm going to assume you have some familiarity with a diode. A diode will pass current in one direction and block it in the other.
Ok, with that as background, suffice it to say that many electronic components present the equivalent of a diode to their power supply leads. So when properly powered, a relatively small amount of current flows into the power lead(s) and things are normal.
When the power is reversed, however, now you have something similar to a forward biased diode and a very large current can flow. This causes damage to the devices themselves, the circuit board traces, the wiring to the units, and so on. The damage is mostly caused by heat generated by very large currents supplied by the reversed jumper cables.
Now some units are reverse voltage protected and they may be OK but many units are not so protected and they sustain significant and nearly immediate damage when the voltage is reversed.