On Starfleet vessels, the tactical officers job is to maintain weapon and shield readiness along with executing firing solutions. These solutions can range from a low intensity phaser beam or to plot a torpedo firing pattern. Security chiefs frequently doubled as tactical officers, though the two roles weren't required to be filled by the same person. (TNG: "Pen Pals", "Masks")
On a Klingon vessel, this crewmember is called the Weapons Officer.