A fuzzy orbit is a way of moving between orbits using less fuel. For example, from an orbit around the earth to an orbit around the moon; it is based on application of Chaos theory to predicting orbital transfers.
If a vehicle is in orbit around the earth; once a month or so, the moon swoops past. Every time it does this, it tugs on the vehicle a little. The trick with a fuzzy orbit is to try to arrange that the vehicle's orbit is such that the moon pulls on it and gives it a little extra energy and momentum each time it goes past. When it finally has enough energy, it will pop over the brink and it can enter lunar orbit with very little fuel use to close the orbit.
Computer searches show that upto 28% less velocity change is needed by the vehicle. Or atleast that is the best that has been found so far. This can translate into considerable savings of fuel.
Fuzzy orbits are extremely hard to plan right now; although new software has been developed to assist with this.
The main disadvantage of fuzzy orbits is that whilst a normal Hohmann transfer orbit will take 3 days, a fuzzy orbit can take months or years. Additionally, you must be reasonably close to the moon to start with for it to perturb your orbit enough for this to work. Still, for freight this manoeuver may save enough fuel to make it very worthwhile.