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).
For this reason, Barrier is often used instead of Heal at mid lane, where there are many champions using Ignite. The lowered cooldown of Barrier also helps against assassins which are common at mid lane. At bot lane, Heal is more common as Exhaust is used more; Ignite is generally only used by supports which want to all-in. Also, with two champions, the healing from Heal is more useful since it can affect two champions at once. The extra movement speed is also more helpful for marksman that want to kite.