The ASE is used for a variety of reasons. It's able to detect hidden messages left by the Drudge, hack computer systems, detect and detonate ghost mines, open organic locks, and decloak the Storm Scarabs.
In The Conduit, John Adams tries to get the ASE, but Michael Ford does everything he can to keep it away from him. Also, Prometheus uses the ASE to contact Ford. And before Prometheus' body was destroyed, he managed to upload his consciousness directly to the ASE.
In Conduit 2, the ASE is used for a number of things, most importantly, absorbing the energies of Progenitor aliens to keep them from Adams. Prometheus then transfers those energies directly into the Destroyer Armor.