From Destinypedia, the Destiny wiki
Absorption Shields are a form of defensive barrier employed by various enemies during combat.
An Absorption Shield manifests as a translucent bubble that surrounds the wielder. Damaging the shield will make it deteriorate, until it is removed. Elemental damage of the appropriate type, identifiable by the shield's color, drains it faster. If a shielded enemy doesn't receive damage for some time, its barrier will recharge quickly. Every race has at least one type of enemy shielded by default but will also have another type of enemy that's shielded whenever the Epic modifier is active (or during certain public events). 
If one inflicts enough damage into a shield regardless of the color, it will deactivate, though this method takes longer, and may waste precious resources and ammo. A high impact weapon of sufficient destructive capacity can deactivate absorption shields in a single hit regardless of its elemental type.
Elemental grenades can take down shields of their respective element by simply detonating next to the target.
Shields gain a unique appearance for each of the enemy races: Fallen are unchanged, Hive gain more oblong and refined shields, Cabal shields are spherical with glowing angular patterns, Vex shields are cylindrical grids similar to the Hydra's, and Taken shields are blackened and "corrupted". Deactivating a shield with a weapon of its corresponding elemental type now triggers an area-of-effect explosion that damages nearby enemies.  Also, during Nightfall strikes and certain other difficult activities, the presence of elemental shields has switched between certain enemy types. For example, Psions no longer have Void shields during the Nightfall strike, but Colossi have Arc shields now.
With the release of Season of the Deep, absorption shields are now the same across all races, but look different depending on the element needed to match it. Void shields are identified by ripples and spirals, Solar shields are identified by flames, Arc shields are identified by electricity, and Strand shields are identified by vertical lines. Immunity shields retain their faction's designs.
Introduced with the expansion The Witch Queen, an Overshield is a type of shield that some enemy subfactions can use. An enemy with an overshield is identifiable by the glow over its body, and a small blue bar under their health bar will show the shield's remaining health. Overshields grant the same resistance to kinetic damage and staggering as absorption shields, but have no specific elemental weakness, overall lower health, and usually do not regenerate on their own, instead requiring new uses of their source to be replenished. Overshields trigger the same perks that work on absorption shields, such as Turnabout.
Enemy shield types
† Indicates enemies that alternate between different shield types.
¥ Indicates that the enemy gains shields in higher difficulty activities or through certain Modifiers.
In addition to this list, Nightmare Hunts will also frequently spawn large groups of enemies (typically the lowest classes associated with the Nightmare's original race) with Solar shields that are unusually resistant to even matching elemental damage. Nightmare Breaker mods, obtained from the gamemode, are required to effectively penetrate these shields.
- The shields of Nightmare minions encountered in Nightmare Hunts all share the Hive design. This remained unchanged with the Season of the Deep shield update.