The Duality Jump Drive is the engine that was fitted to the Nova 5 in Series II episode "Kryten" and in the first book Infinity Welcomes Careful Drivers. From what the book states, the Drive has something to do with quantum mechanics and indeterminism and, when measuring electrons, they can be in two places at once.
Apparently, when you made a Duality Jump, it seemed that you temporarily coexisted at two points in the universe and then you 'chose' which one of these points to 'be' in. In this way you could leapfrog across the universe, not bound by the limits of space-time.
From Red Dwarf's location in the first book when they first find the drive, the crew could get back to Earth in around 3 months. The Nova 5 Jump Drive ran on Uranium 233 which, luckily, can be synthesised from Thorium 232.