Barrier is great for absorbing the burst of enemy champions. Whether used on a squishy mid-laner or a tanky top-laner, a well-timed Barrier will help escape from tough situations.
Barrier can be used despite any Crowd Control with the exception of suppression.
Many consider Barrier to be vastly inferior to Heal, because it only affects one person, offers no speed boost, and the shield is temporary. However, Barrier is not affected by Grievous Wounds, has a shorter cooldown, blocks more damage (against a single target), and can be used while you're still at full health (good against 100-to-0 burst).