Sir John Falstaff was Prince Hal's sidekick in Shakespeare's play Henry IV. He was plump, witty, and self-indulgent. Because of this, the word falstaffian is used to describe a person with this sort of jolly personality.
But originally, the name Falstaff had a different meaning.... In Shakespeare's plays Falstaff was not popular with the ladies; to emphisize this quality Shakespeare gave him a punish name, formed from the contraction of two words: 'false' and 'staff'. The word 'penis' did not come into use until 1693, so various euphanisims were used in its place; in this case, the false-staff refers to a weak member.