Adding a cup (or more) of starchy pasta-cooking water is what actually creates the unctuous texture of aglio e olio, bringing together the seasoned oil and the cooking water into an emulsified, creamy sauce.
You may be familiar with the term al dente, or “to the tooth,” as a way to describe pasta’s ideal doneness. However, with this technique, the pasta is traditionally cooked only halfway (known as al chiodo, or “to the nail”). It is then drained, added to the pan with other ingredients (which typically include some form of fat) and a lot of starchy pasta water, and simmered until al dente and the liquid has reduced into a creamy sauce. This last step in the process is known as mantecare.