The Boner on the Edge of ForeverPriapism is a medical condition, a sustained and eventually painful erection that will not cease. It is not related to erotic feelings or a particularly effective stripper, but is usually the result of either a change in the blood (clotting, blood diseases) or medications (anti-impotence medicine and increased dosages).
The right thing to do in this situation is get over your embarassment immediately, put on some clothes, and get over to a hospital, where they will drain the penis of the clotted blood with an injected needle. It sounds bad, but not as bad as it could be; leaving your penis in a Priaptic state will lead to permanent damage and a very good chance of continued impotence.
Ironically, the condition is named after the Fertility God Priapus, likely because he is usually depicted with a stunning endowment and often erect.