Marking the mobs before a fight not only make a sign for other members to know what's the order of kill, it also speed up the fight.. I'll provide some sequence example:
Without Marking:
1. Tank initiates
2. DDs target tank, use "Target's target", or check the game screen to target the tank's target manually.
3. DDs start fighting
4. Repeat

With marking:
1.Tank marks order number
2.The DDs had already targeted number 1, mages have their target set to 2 or onwards for sleep.
3.Tank initiates, DDs and mages can adjust their attack / sleep to register right after tank's action on their targets.
4.Mob 1 dies, immediate switching of targets from DDs to continue on mob 2.

Overall marking reduces a lot of idling time for whole party to waste on "Whats the tank gonna do next?" situations.