The Ankle Bone's Connected to the Shin Bone

After a few weeks of my car dashboard telling me to "Check Stabilitrak" (whatever that is) and "Check Traction Control" (that doesn't sound good), I had a repair appointment at the dealership.  After taking an hour to let a computer diagnose the problem, the service technician told me that the EGR Valve was faulty.  According to Wikipedia, "EGR works by recirculating a portion of an engine's exhaust gas back to the engine cylinders."  This tallies with what the technician told me.

Now, I know next to nothing about cars, especially since I learned to drive back when cars were easier to fix and mechanics were smart enough to diagnose faults without using a computer, but how does a traction warning (which sounds like something to do with the wheels, axles, or steering) end up as a wonky part of the exhaust system?

The technician said that the car's computer (something else new since I learned to drive) registered the fault with the valve and then tried to compensate for it, which resulted in the traction warning.  I can vaguely understand that (trying to compensate), although it still sounds like a "black box" is somewhere between the exhaust and the tires.  This is another reason I prefer working with plants:  no moving parts.