The targeting laser is not so much a weapon as it is a tool. When you fire a targeting laser, a green laser shines from it and displays a target reticle where you are aiming for all of your teammates. This target is functionally the same as a targeting beacon, and it remains there as long as you are holding down the trigger. All players carry a targeting laser by default, and it does not take up a weapon slot. Additionally, it won't appear when you cycle through your weapons; you need to press a specific key - L by default - to switch to it.
Usage
There are three uses for the targeting laser that are the most common.
Enemy warning
Ironically, this is the most common use of the targeting laser, even though it has nothing to do with the targeting laser's actual functionality. When a player on a team sees an incoming enemy that the rest of his team might not have noticed, it's a common practice for that player to shine a targeting laser in that general area to warn his teammates that an enemy is over there. This can be especially useful to warn your team about incoming cappers who are trying to remain unseen until they come in for a cap.
While this is the most common use of the laser, it still isn't used outside of pub play as voice communication software much more convenient ways to inform your teammates.
Missiles
Missiles can be locked on to the target reticle created by a targeting laser. The benefit of this is that flares will not affect the missile if it is locked on to a targeting reticle. However, pay attention to make sure that you are actually locked onto the targeting reticle and not the object itself. For example, if a targeting laser is being shined at a turret, you could lock onto either the turret via its heat signature or the targeting reticle. If you are locked onto the turret itself, flares will still affect the missile. Sometimes it can be hard to determine which of the two you are actually locked onto, so be warned that you may run into the problem if you use this tactic.
Aiming marker
Just like targeting beacons, the targeting laser shows an aiming marker that shows your teammates where they need to aim to hit the target. This aiming marker takes into account all factors, including current velocity and the weapon being used. This is usually only done in public servers, because it's a waste of time for a player to actually have someone use a targeting laser in a competitive game. Even in pubs, it's mostly only done by unskilled players, because most skilled players have mastered their weapons well enough to accurately aim them without an aiming marker.