What is origin of the idiom blow your wad?

The origin comes from the days of muzzle-load firearms: both big and small. To ensure a good seal for the black powder, it was common practice to place an amount of cloth (called wadding) between the powder and the projectile. If the wadding comes out of the gun after the projectile, then the gun has completed a full and proper firing, which is what you want.

Thus, blowing (or shooting) one's wad (or load) comes to means a full and complete discharge or release, and the terms can be used both inside and outside of sexual circles (in the latter case, saying someone shot their load can mean they put everything they had left into an effort).