In purely scientific terms, Power refers to the amount of work that can be done per unit time, be it mechanical or electrical. However, in colloquial terms, power refers to electrical energy used to run technological devices. Power is generally supplied in the field by Power plants or Advanced power plants.
In military bases, sufficient power generation is a necessity. First, although productions structures often have backup generators allowing them to continue operation without external power, these backups are limited in capacity; so construction yards, war factories, barracks, and other such strutures operate far more slowly when without power.
Also, many advanced structures require far greater amounts of power to operate, and will cease functioning in a blackout. Upper-tier base defense systems such as the Tesla Coil or Obelisk of Light need enormous amounts of power, and will cease to offer protection if they are not powered. Also, Radar will not work without power.
Additionally, power outages can undermine a base's integrity; and buildings will undergo damage as long as power output is not equal or surpassing the demand.
As power is a vital necessity for many important military functions, commanders can significantly weaken their opponents by attacking their power plants. Plants are generally very weakly armoured, so it is advisable to build more plants than necessary to lessen the chances a surprise strike with blind and paralyze a base.