Agent Brown was one of the Agents, working together with Jones and Smith.
He was the first agent to have a prominent role, as the agent who chased Trinity on the rooftops. He appeared in the the background from then on, until he injected Morpheus with a program (in the form of silver liquid) , while the rebel was interrogated by Agent Smith.
He, like the other two Agents , was again temporarily killed when Neo blew them away with a minigun mounted on a B-212 helicopter. After Neo blew up Smith , both he and Agent Jones ran away and were never seen again. He may have been deleted and replaced with superiors agents or, presumably, had been updated to become Thompson, Jackson or Johnson. He and Jones' fates are not made clear in the films.