I doubt whether any Hogwarts students ever found out more about the Hogwarts grounds and Hogsmeade than we did.... And that's how we came to write the Marauder's Map, and sign it with our nicknames. Sirius is Padfoot. Peter is Wormtail. James was Prongs.
-- Remus Lupin (PA18)
Definition
Padfoot was a nickname of Sirius Black, created and used by his friends at Hogwarts who knew he was an animagus.
Commentary
Etymology
"Padfoot" = A large dog, variously said to be a ghost, spirit, or monster, supposed to guard graves and to terrify travelers (NSOED).
Sirius was given this nickname because his animagus form was of a large dog.
Notes
Rowling was asked how she came up with the nicknames for the Marauders:
How do you think of all the names, like Moony, Wormtail, Padfoot and Prongs?
Those names all came out of the creatures that they turned into. I had a lot of fun with those. Wormtail was the most difficult one. My sister loathes rats and her problem with them is their tails, so that is what gave me the idea. (JKR: News)