A phaser emitter was a key component in starship and hand-held phasers. The emitter was equivalent to the "barrel of a gun", as it was the focal point from which the phaser beam ("the bullet") was fired.
From 2245 to 2270, ship-mounted phaser emitters were built into the hulls of Starfleet vessels and were operated from a control room by a small crew as a backup to bridge control. (TOS: "Balance of Terror")
In the 2270s, phaser emitter designs had improved and the new design routed power directly from the warp engines, which increased their effectiveness and strength. The only drawback was that if an antimatter imbalance occurred, the phasers would be automatically cut off. (Star Trek: The Motion Picture)
Ship-mounted emitters were typically arranged into phaser banks. The normal arrangement was one or two emitters to a bank. (Star Trek II: The Wrath of Khan) Phaser banks and their emitters were later replaced by phaser arrays in the 24th century on more modern starships. Smaller vessels such as shuttlecraft and Maquis fighters continued to use phaser emitters, however. (TNG: "The Outcast", "Preemptive Strike")
In 2372, the deflector of the USS Defiant was modified to perform as a single-shot phaser emitter when the ship was under attack from a Jem'Hadar attack ship in the atmosphere of a class J gas giant. (DS9: "Starship Down")
In 2375, Nog, acting as a representative of Miles O'Brien, bought a phaser emitter from the USS Musashi in a convoluted trade that also involved the USS Sentinel, in order to eventually acquire a graviton stabilizer. (DS9: "Treachery, Faith and the Great River")
Phaser emitters formed part of the main component of hand phasers.