A piece of information lacking in the other definitions is the fact that priapism, while sounding like fun, is extremely painful and requires surgery (aka draining the blood out) to fix. Priapism can be caused by several things, including the bite of certain venomous creatures on or near the genitalia, overdosing on a "male enhancement" supplement, spinal cord or brain injuries, clots, or sickle-cell anemia. Note that if you have been able to fap or bone your gf/wife/prostitute for four hours plus, you do not have priapism. If not treated properly, priapism can result in loss of genitals or possibly life.
Guy: Dude, I think I took to much Viagra. My dick feels like it's gonna blow!
Dude: That's priapism. It's not good, guy. You need to go to the hospital!