Shrouds are useful items that allow you to gain an edge in an upcoming battle. They should only be used for difficult boss battles and later in the game, because they are hard to come by:
a) Deceptisol makes the leader invisible to the enemy. If you touch an enemy while under this effect, you will automatically gain a Preemptive Strike on the enemy. Note that there are exceptions (like boss battles).
b) Fortisol gives you Faith, Bravery and Haste for the next battle.
c) Aegisol gives you Protect, Shell, Veil and Vigilance for the next battle.
d) Ethersol completely recovers your TP gauge. Shrouds can only be used when not in battle. Press L1/LB to bring up the Shrouds menu, choose the one you want to use and press X.