The Mars Rover Curiosity is powered by nuclear material, a stable or non-fissile isotope of the radioactive element Plutonium Pu-238, meaning its nucleus does not breakup in a chain reaction upon triggering.
As all radioactive materials do, the spontaneous but safe release of sub-nuclear particles in the case of non-fissile materials also releases heat. The heat can be used to generate electricity, warm plumbing and recharge what are essentially cell phone batteries by well known mechanisms which are being currently used on Curiosity, in an improvisation over missions since Apollo.
At issue is how can a standard but contained nuclear fission reactor which generates electricity by using a turbine powered by steam from fission heat which is orders of magnitude larger than the natural heat from the decay of Pu-238 be used for both power and propulsion on space missions, because non-fissile or any radioactive material refinement is expensive and the cost-benefit does not work out besides on test missions such as Curiosity (it is for this obvious reason that it cannot be used on cars, for example, even though Curiosity is being compared in size to passenger cars).
The problem of mounting a small nuclear fission plant for power as payload to be used on a Moon or Mars base is straightforward, a matter of scale effects, though it has never been tried before.
Nuclear propulsion, however, is not as simple a problem to solve because the reactor per se is not sufficient to generate the periodic thrusts necessary to alter the speed and navigate a space craft in flight, whether that be in orbit or in travel between two heavenly bodies.
Thrust in vacuous space requires ejection of gaseous material to generate an equal but opposite reaction in any given direction. The combustible gas is hydrogen and it burns in oxygen producing water. This basic chemical phenomenon implies that somehow sufficient hydrogen and oxygen must be produced aboard a spacecraft, on demand if feasible, from a power system, for them to recombine in combustion to produce the desired thrust by controlled combustion and ejection.
A technology which is most amenable and available as a power-propulsion hybrid for both onboard power and thrust using water as payload, building-in dissipation of the water resource after each thrust, is the regenerative fuel cell technology in development at Lawrence Livermore National Laboratory of the Department of Energy.