He was the first Agent to have a prominent role, being the Agent who pursued Trinity on the rooftops. Afterwards, he would constantly appear alongside Agents Smith and Jones until the moment he injected Morpheus with a program (encoded in some form of silver liquid). Upon Agent Smith's orders, he would then leave with Agent Jones, allowing Agent Smith to interrogate the rebel alone.
During the Rescue of Morpheus, the other two Agents and him were taken by surprise and temporarily killed by Neo using a minigun mounted on a B-212 helicopter. The rescue efforts culminated in Neo waking up as The One and blowing up Agent Smith. Both he and Agent Jones ran away and were never seen again.
The Oracle explains how programs are deleted when they are replaced by a better program. And while the exact fate of Agents Brown and Jones are unclear, the appearance of the upgraded Agents (Thompson, Jackson, and Johnson) suggest that they were simply deleted and replaced.