OverviewThe Enhanced Defense Intelligence or EDI (pronounced ee-dee) for short, is a Cerberus built Artificial Intelligence(AI) and is vastly more different from the normal Virtual Intelligences VI) found on normal ships or technologies around the galaxy.
EDI was mainly built as a Intelligent Combat program to battle the Reapers aboard the Cerberus Frigate the Normandy SR-2. It is partially built from the ruins of "Sovereign", the reaper that nearly destroyed the Citadel in the battle of the Citadel in the year 2183. This is the reason why it is even conceivable that EDI is capable of drawing combat responses against the vastly advanced intelligences of the Reapers.
Besides the primary purpose, there are other secondary purposes for which EDI is around, one of them being to report activities and conversations on the Normandy and to report them to the Illusive Man who is the head of Cerberus.
Being an AI there is very obvious prejudice from most of the crew against EDI since the only things AI have brought to the galaxy in the form of the Geth and the Reapers are considerable grief. Even to the extent that Cerberus themselves have taken precautions in case EDI goes rogue by limiting the amount of functions she has on the vessel.
 PersonalityEDI initially acts and talks exactly like how a normal VI would when the Mormandy SR-2 flies on her maiden voyage for the first time, however, with prolonged interaction with the various crew members and in particular Commander Shepard and the ship's Helmsman, Jeff 'Joker' Moreau, EDI starts to develop her own personalities and loyalties. In fact when the collectors abduct the crew of the Normandy SR-2, EDI chooses to specifically use Joker to connect her to the Ships main control systems rather than anyone else. And in turn she does everything possible to save at least Joker's life.
She also starts to show changes in her speech patterns with joker by trying out different jokes on him that often turn out to sound too serious rather than funny. Only going to show that EDI is in fact very capable of being considered a sentient being herself who learns and can make decisions that are off the primary or secondary objectives of a normal VI.