Basically, the more you know, the faster you go. An on-board computer allows the drivers to analyze what they are doing, and how to improve. If you have two drivers, they can compare their laps and see where each one gains or loses time, and why. A driver can compare his best lap to other laps and see where the difference is.
Drivers can try different techniques or styles and see what difference they make.
Several customers report substantial improvement in lap times from analyzing braking performance alone. Engine data can be very helpful for increasing both performance and reliability. Some racers also monitor fuel pressure and nitrous pressure for the same reason. One customer reports that the system saved him an engine, by showing him a problem before the engine was destroyed. Engine RPM is a big help, especially combined with g readings and throttle position.