Agent Brown was one of the sentient 'Agent' programs. He was the first Agent to have a prominent role, as he was the one that chased Trinity across the rooftops.
It's mostly background work from then on in, until he injected Morpheus with a codebreaker program (in the form of a silvery liquid) while he was being interrogated by Agent Smith. He, like the other two Agents, was again temporarily slain when Neo blasted away with a chopper-mounted minigun. He failed to kill Neo and was not seen again. It is possible that he was deleted and replaced by the Upgraded Agents, or, conceivably, was upgraded himself to become Thompson, Jackson, or Johnson.