Willie the Pimp is one of many odd characters Frank Zappa created. In this song, we hear about his exploits running his operation out of the Lido Hotel on Coney Island.
A vague explanation of the song's origin appears on Frank Zappa's outtake and extras album Mystery Disc, released in 1998. A track on that album is called "The Story of Willie the Pimp," which is a strange conversation between two women who are apparently speaking with Zappa. Credited on the album as Annie Zannas and Cynthia Dobson, they talk about setting a guy up to meet a prostitute that doesn't exist. According to Zappa lore, this is the conversation that inspired the song.
The vocals on "Willie the Pimp" are from Captain Beefheart, who was a friend of, and collaborator with Zappa from the time they were teens.