The Aegis refers to two things: the barrier and pocket dimension that acts as Earth's first line of defense against extradimensional/extraterrestrial attacks, and the organization responsible for ensuring those attacks are suppressed efficiently and effectively.
The Aegis Field
Enemies that attempt to attack a planet by space would be met by a translucent barrier. The barrier around the globe is maintained by Heishan. Emissaries are able to create Aegis fields at varying sizes to contain their enemies, they act like pocket dimensions to reduce casualties and damage.
The Aegis Company
They manage known and willing emissaries to most effectively use their abilities to keep their world safe. They try to keep track of how many emissaries are in certain locations and spread them out to maximize their defenses.