Finishing the pasta in the sauce not only allows the neutral-tasting pasta to absorb some of the sauce and its flavor, but it also makes the sauce viscous enough to cling to the pasta, as the starches the pasta sheds during the cooking process thicken the sauce.
This method works especially well with thin pasta sauces, such as those with broth or wine as a base (although it definitely also works with your typical heat-and-eat marinara). You can use it with any shape of pasta, and you can finish the cooking process either in the pasta pot or in the sauce pot.
No matter what type of sauce you are making, you should always reserve some of the pasta cooking water to adjust the consistency of the finished sauce to your liking.