A TAG shows the predicted movement of a guard on the next enemy turn. Their predicted path is shown in the user interface as a series of white triangular arrows, similarly to when observing the guard's movement, except their interest point is not also shown by the TAG.
Guards can be TAGged using a TAG Pistol, or the program Wisp. Once a guard is TAGged, they remain TAGged for the rest of the mission, unless the TAG is removed by the program Lightning.
TAGging guards is extremely powerful: it shows you where they will move on their next turn, every turn, without spending AP to observe them. Just as importantly, it also shows you where the TAGged guards currently are, even in the fog of war, as long as they aren't stationary. TAGging is particularly helpful when guards are hunting, since their movements are less predictable.
Ideally, you can TAG every guard in the facility. With full information about where every guard will move, it is almost always possible to leave your agents in cover from them; on the other hand, you can also see whether any guards will enter any given room on their next turn, so sometimes you do not need to end your turn in cover at all.
Keep in mind that the path shown for a guard will not be accurate if the guard sees something suspicious during the enemy turn. The path shown in the user interface also does not tell you whether a guard will peek (or whether a drone will scan) at the end of their movement, so sometimes you may still want to observe a TAGged guard's movement to see their interest point.