A rising star refers to the penis as it goes from sleeping to erect (or somewhere on that spectrum).
Rising star is so called because the penis begins to rise. Often this is caused by the hint of sex, talking about sex, or seeing something erotic. It can also happen spontaneously, especially in pubescent boys who suffer (or enjoy!) many rising stars on a typical day.
Bob sat looking at Miss Jones writing on the blackboard. His rising star was obvious to his mate David, who reached under the desk and fondled it.
Soon Bob's rising star was a full blown stiffie and he really wanted to blast a load.