Why add pasta water to pasta sauce?
I believe the primary reason is that the pasta water is already hot. When you need to thin your sauce on short notice, you add hot pasta water and it will not cool down your sauce. Secondary benefits are:


The pasta water has nice salinity, so you're not diluting the salinity level of the sauce. This assumes you salted your pasta water. You did, right?
There is some starch in the pasta water. However, since the pasta water has already achieved a high temperature, any thickening benefit would already be achieved. If your pasta water is anything like any I've ever seen, it's just about as runny as any other water. So this benefit is probably negligible. Perhaps it has more of an effect once the pasta water added to the sauce has reduced.