Two possible Treksplanations for mass reduction devices:
1. Gravity is a function of the interactions of gravitons in various bodies of mass. If you shield an object from the effects of the gravitons in the masses around it, you reduce the effective mass of that object (or, from the object's perspective, the effective mass of the universe around it).
2. As an object approaches the speed of light, it approaches infinite mass and zero time. The increase in mass and decrease in time are inversely proportional. If you bombard the object with chroniton particles, you increase the object's time and effectively mitigate the increase in mass, possibly up to the point of actually decreasing the effective mass.
These two might actually be viewed as the same thing, if the mechanism for shielding an object mentioned in 1 above is by bombarding it with chronitons as mentioned in 2.