The Twins are two of the Merovingian's henchmen in The Matrix film trilogy, originating from the machines' second attempt at creating a viable matrix. It is unknown why the Twins became Exiles but they are apparently very infamous with the Agents, who waste no time trying to attack them during the freeway chase.
Rumors emerged before the second film's release that their reason for becoming Exiles was that their programming became infected with a virus, which the Merovingian was able to remove (although not before it damaged their appearance and emotional subroutines, resulting in their emotionless demeanor); scenes from the chase agree. Link cannot work out their program type and calls them simply "The Twins". Some suspect they were former Agent programs that became exiles when replaced with the more "modern" Agents.