Exiles were originally programs that had a purpose before they were threatened with deletion. They escaped in the Matrix (most have used the Trainman).
The Merovingian Edit
The most powerful and influencial exile in the Matrix is The Merovingian, who was formerly an OS is a prominent ruler of an underground empire. Most of his henchmen are exiles, most notably the Twins.
in the Matrix most exiles disguise themselves as normal humans and are hunted down by Agents who want to prevent any deviations within the Matrix.
Most of the Merovigian exiles were formerly part of the former Matrixes that took the form of supernatural creatures (i.e. vampires and werewolves).
The General and his commando squad were formerly sentinels that attacked the city of Zion and refused to stop attacking. This led to them estgablishing themselves a real world base called Stalingrade and were able to gain acess to the Matrix. When in the Matrix, they appeared as armymen to signify their former purpose as warriors for the machines.