(covers information from several alternate timelines)
Phaser banks referred to the phaser weapons mounted aboard Federation starships. (Star Trek: The Original Series; Star Trek: The Animated Series) They were utilized by Starfleet as early as 2233. (Star Trek)
Each bank contained one or more phaser emitters from which the beam energy was actually released but which shared common power sources and targeting systems.
The main banks were located on the lower half of the starship's saucer section, forward of the sensor dome. Additional banks were located on the ship's stern, above the shuttlebay. Port and starboard banks covered the ship's flanks. (TOS: "Arena"; TNG: "Datalore"; ENT: "In a Mirror, Darkly, Part II")
In the 2270s, a new system was developed, tying the phasers directly into the main reactor. While increasing phaser power, it had the disadvantage of cutting off most of or all phaser power if the reactor was damaged. (Star Trek: The Motion Picture; Star Trek II: The Wrath of Khan)
By the 24th century, the number of emitters in each bank had been increased to the point where they were laid out in long strips called phaser arrays. (Star Trek: The Next Generation) However, the term "phaser bank" was still used, particularly in reference to units with smaller numbers of emitters. (DS9: "The Maquis, Part I")