-a more sophisticated way of saying "sucking him dry". Basically, men are continually producing semen, and after several days the urge to cum becomes unbearable. So his gf/wife makes him ejaculate via fellatio/intercourse (the ejaculation is often both powerful and plentiful), then blows him for several more minutes, sucking out the rest of his love juice and swallowing it. The last steps are highly recommended to insure he is completely dry and empty.
-"Pipes" refer to the long, twisting canals of the interior male genitalia.
Daniel had gone to the East Coast to visit grad schools and did not get a chance to masturbate even ONCE during the trip. When he got back to Berkeley, Jamie, his fiancee, sensed he needed to shoot badly so she sat him down and immediately got to work cleaning out his pipes.