The mind flayer is a creature original to D&D and, like many of Gygax's early creations has a "does what it says on the tin" style name. To my mind, it's one of the better such names - although almost anything is better than, say, "lurker above". The look of the creature is obviously reminiscent of H.P. Lovecraft's Cthulhu, and Gygax stated that it was inspired by the cover of a book by Brian Lumley that does, indeed, feature a being from the Mythos. But, as it happens, it isn't the Big C himself that's on the cover, but a chthonian, a creature with a similar name, to be sure, but actually rather different. Still, it has tentacles and this, seemingly, was enough.
1E
The mind flayer goes through relatively little change in physical appearance through the various editions of the game, to the extent that the few changes that are apparent could easily be put down to variations between individuals of the same species. Even the clothing doesn't change much, with the race clearly having a preference for robes and insisting on a skull motif somewhere on their belt.