The Aegis Shield spawns in the Templar's Well after the waves of Oracles have been completed.
It also appears in the Vault of Glass itself during the Gatekeeper Fight and the Atheon Fight.
Using the Aegis Shield
The relic: Aegis serves a few uses.
First, it gives some alternate melee and aerial attacks. The light melee attack allow for rapid movement and some damage. The Heavy melee attack is a longer dash attack that does more damage. The air borne attack has the wielder come down for a massive AoE attack with lots of damage.
The relic can also generate a shield. Using the "grenade" energy, the Relic Bearer can generate a shield. This will block incoming projectile fire and cleanse anyone who has the Mark of Negation. For this phase of the fight, it is the only way to clear the Mark of Negation or Marked by the Void during the Atheon Fight.
Just like the Hive Blades, the Super ability is constantly charging. It will build up faster when the Relic is used to clear out the enemies around. When used, this launches a Rocket-like projectile. This projectile is the only way to remove the shield around the Templar.