A grenade launcher was any of a number of devices used to propel a small bomb called a grenade. Grenades were often thrown, but a grenade launcher could be used when greater range and accuracy were required than could be achieved by a throw.
In 2267, Captain James T. Kirk found a Starfleet-issue grenade launcher that had survived the Gorn attack on the Cestus III colony. With it, he was able to force the Gorn to decamp so that his landing party could escape their ambush. Presumably, the Gorn were not expecting to meet such determined resistance. A grenade was launched by Kirk to impact at a range of about 1200 yards; which, according to tactical officer Kelowitz, was "a little close". At that range, there was little shock wave or debris. (TOS: "Arena")
The device was tube based and would have been called a mortar by a 20th century soldier. The ammunition had no visible guidance system or aerodynamic attachments. Kirk however made adjustments for range and azimuth on the tube. This would suggest the presence of some type of a guidance system.
In the computer games Star Trek: Voyager - Elite Force and Star Trek: Elite Force II standard and enhanced compound grenade launchers at Memory Beta, the wiki for licensed Star Trek works are available for the player. They are a heavy weapons that can fire energy grenades with time delayed detonation, 'sticky' grenades with proximity detonators, or remotely triggered grenades.