Existem algumas teorias circulando na internet ...
George Orwell's 1984 :
A tribute to George Orwell's Room 101 in 1984, where a prisoner is subjected to their worst phobia, and has subsequently been used in popular culture to signify a room where an item can be placed to never be again found. Neo has in turn been placed in room 101 by the machines, as they do not want 'The One' to be discovered.
Computadores (binários):
101 actually appears a number of times in all three films, and though no one knows exactly what it means (if anything), the popular explanation is this: 101 is binary for 5 (which to a computer is the sixth number because computers count from 0), and the events of the three films take place in the 6th interation of the Matrix. Neo is the sixth One, this is the sixth time the machines have destroyed Zion, etc. We learn that this is the sixth iteration from The Architect's conversation.
e, claro, há o óbvio: Trinity está na sala 303 (Trinity = 3), e o número do apartamento de Neo é 101 (Neo, "The One" = 1).