The reactor is the heart of any ship in the FreeSpace universe, providing power to all its systems. Terran and Vasudan reactors are fusion based, and run off deuterium collected by Anuket and Zephyrus gas miners.
Vasudan reactors are known to be particularly efficient, and provide the power for the GTCv Deimos-class corvette, which, tonne for tonne, produce more energy than any other vessel in the Allied fleet.
Power from the reactors on fighters can be shunted between the various subsystems of the ship to maximize their performance using the ETS, or Energy Transfer System. A similar system probably exist on capital ships, as the GTVA Colossus was able to increase power to its beam weapons while battling with the SJ Sathanas. This action is known to be extremely dangerous, as the Colossus overloaded both its secondary and tertiary reactors in doing so, and the NTC Righteous was completely destroyed by a reactor overload under similar circumstances.
Data on Shivan reactor systems is limited, but they are apparently quite volatile, as it was the destruction of the SD Lucifer's five reactors which led to the destruction of the ship itself. Destroying the reactors on other Shivan vessels, however, does not destroy them, so this may have been a peculiarity of the Lucifer design, or as a result of their being destroyed while the vessel was in subspace.