The TR-116 rifle is a hand-held rifle-type weapon, a projectile weapon developed by Starfleet Security for use in dampening fields or radiogenic environments where conventional energy weapons would be useless. The rifle fires a chemically propelled tritanium bullet. A working prototype of the weapon was developed, but Starfleet opted not to produce the weapon after the advent of the regenerative phaser. The TR-116 could be operated by both right and left-handed shooters.
In 2375, Science Officer Chu'lak used a TR-116 rifle to murder fellow Starfleet officers Hector Ilario, Greta Vanderweg, and Zim Brott aboard Deep Space 9. Chu'lak modified the rifle with a micro-transporter, which allowed him to beam the bullet into another room, only 8-9 centimeters from its target. An exographic targeting sensor allowed Chu'lak to scan through walls and target victims anywhere on the station from his quarters.
In the non-canon Deep Space Nine Mission Gamma novel Lesser Evil, Lieutenant Sam Bowers tells of his experiences aboard the USS Budapest during the Battle of Sector 001. The Budapest was one of a handful of Starfleet vessels equipped with prototype TR-116s. When the Borg attempted to assimilate the ship and its crew, Bowers led a security team equipped with TR-116 rifles through the ship, with orders to eliminate any and all Borg drones. Because the weapons used projectiles instead of energy beams, the Borg's deflector shielding was useless, and the Budapest crew were successful in stopping the Borg.
Though these events were never mentioned in "Field of Fire", the statement about projectile weapons being effective against the Borg is supported in part by the scene in Star Trek: First Contact where Jean-Luc Picard uses a holographic Thompson submachine gun to kill two Borg drones. It is unlikely that Borg have any kind of kinetic energy shield, as there have been dozens of incidents in which Borg drones have been killed by blows from rifle butts or bat'leths multiple times, and no adaptation was seen.
In the novel A Time to Heal, a Starfleet security sniper used a TR-116 to stun Tezwan guards. It was noted that the gun could "shoot through walls", indicating that Chu'lak's modifications may have been adapted for field use.
The fact that projectile weapons have not become standard-issue is probably a strategic decision by Starfleet; the limited environments and adversaries for which projectile weapons are an advantage over phasers are not sufficient in number or threat to justify the logistical problems of stocking or replicating ammunition. It may also be that the TR-116 is too close to being a strict assassination weapon to comfortably issue, whereas phasers can function as tools in addition to its use as a weapon.
John Eaves has stated that it uses a .30 caliber round. 
In the novel Star Trek: Destiny - Lost Souls, David Mack describes the TR-116 as using 10mm Monotanium slugs. This addition of information could explain that the rifle comes in several different calibers (like many modern firearms) or that it itself can be altered to fire different types of ammunition through a function on the rifle or a quick-conversion/part-swap kit.