The Infinite Improbability Drive is a faster-than-light drive. The most prominent usage of the drive is in the starship Heart of Gold. It is based on a particular perception of quantum theory: a subatomic particle is most likely to be in a particular place, such as near the nucleus of an atom, but there is also a small probability of it being found very far from its point of origin (for example close to a distant star). Thus, a body could travel from place to place without passing through the intervening space (or hyperspace, for that matter), if you had sufficient control of probability.
The Heart of Gold was the prototype ship for infinitely improbable travel. The principle is that as its drive reaches infinite improbability, the ship passes simultaneously through every conceivable and inconceivable point in every conceivable and inconceivable universe (in other words, when one activates the Infinite Improbability Drive, the ship is literally everywhere at once). It is then possible to decide at which point you actually want to be when improbability levels decrease.
The Infinite Improbability Drive is also the Golden Bail of Prosperity in the Wikkit Gate. It is stolen by the white Krikkit robots, however, it was returned and the Heart of Gold returned to operational status.
There was also an earlier attempt at using the improbability drive, Starship Titanic. In theory, the infinite improbability drive would make it infinitely improbable that anything would go wrong. It was not successful, however, ending in a "Spontaneous Massive Existence Failure." This was because, in these earlier times when the nature of improbability was less well understood, it was not appreciated that any event that is infinitely improbable will, by definition, occur almost immediately.
Unfortunately, human beings are accustomed to travelling at normality (probability 1:1), and can be fairly distressed by events around them whilst the improbability drive is working: losing limbs, turning into sofas, planets spontaneously becoming fruitcakes, nuclear missiles metamorphosing into sperm whales and bowls of petunias. The starship Heart of Gold was somewhat insulated against this by having an improbability-proof drive room, allowing the pilots to remain more or less normal during the flight.
The most important side effects of infinite improbability travel were that hyperspace express routes became largely obsolete - removing the reason for which Earth was demolished - and that the History department of the University of Maximegalon finally gave up trying to figure out the universe, as completely impossible things were increasingly commonplace.