ASC uses the antilock brake sensors on each wheel to make sure that all 4 wheels are spinning at about the same RPM. If a rear wheel is spinning faster than the others, the computer says "DOH! He's spinning a wheel!" and modulates the fuel supply, reducing the power to the wheels, to eliminate the spin.
As Codex said, leave it on unless you have a good reason to turn it off - racing, track, stuck in the mud or snow, etc.