In the case of a chemical rocket, for example, the reaction mass is the product of the burned fuel shot backwards to provide propulsion.
The velocity of a body is easily changeable, but in most cases the mass is not, which makes it important.
Most rocket engines use light-weight fuels (liquid hydrogen, oxygen, or kerosene) accelerated to supersonic speeds.
However, ion engines often use heavier elements like xenon as the reaction mass, accelerated to much higher speeds using electric fields.
This means that rockets stop accelerating as soon as they run out of fuel, regardless of other power sources they may have.