Energizers were important power-generation components on Constitution-class starships. If the energizers were out, because of damage from weapons fired by a foe, the ship resorted to auxiliary power for powering the ship. In that situation, the ship had limited use of its phasers and transporter.
Energizers could be used for the purpose of re-amplifying dilithium crystals which had been drained by overexertion of ship's systems. The Enterprise was forced to do this in 2267, after an encounter with a powerful and disruptive cosmic phenomenon. Captain Kirk ordered Lieutenant Charlene Masters to begin re-amplification immediately, but as she was in the midst of doing so, the crystals were stolen by Lazarus, an unstable individual whom the crew had discovered on the surface of a barren planet. (TOS: "The Alternative Factor")
Later that year, while the Enterprise was engaging in battle with an extremely powerful planet-destroying weapon, deck seven reported a power failure in the main energizers, necessitating the implementation of emergency procedures. (TOS: "The Doomsday Machine")
In 2285, Commander Scott was forced to bypass the Enterprise's main energizers, after they were severely damaged in battle with the USS Reliant, which was under the command of Khan. (Star Trek II: The Wrath of Khan)