Targeting System
The targeting computer is used by the active sensors (long and short range), the photon torpedo tubes and the phaser banks.
Each of these systems can be individually targeted on an object, or be tied together in groups to allow multiple systems to target objects quickly. For example, the science officer might be using the short range sensors to scan a vessel, while the tactical officer might be aiming the weapons at another target. The tactical officer has tied all of the phaser banks together as one group, so when he selects his target all of the phaser banks lock on to it.
Equally each phaser bank could be assigned different targets if required (though this would probably require a lot of team work).
Each target group can be set to auto target torpedoes, this means that if any photon torpedoes (or enemy equivalent) are registered by the passive scanners, then the target group will automatically lock on to them and start firing in an effort to destroy them (and protect the ship). If the passive scanners are offline, then this feature will not work.
Power Requirements
The targeting computer draws 10MW of power whenever it is online. Although only one is required it would probably be advisable to install backup computers on larger ships given the criticality of this system during combat.