A Mainframe refers to a computer system, both of which were used by the Machines and the Zion resistance. The Zion Mainframe acted as one of Zion's defenses. Each hovercraft captain is given access code to the Zion mainframe computer, making them valuable targets for the machines and their agents, enabling them to enter Zion, the home of the human resistance.
The traitorous operative known as Cypher secretly made a deal with Agent Smith to help capture Morpheus who knew their hovercraft's access code to the Zion mainframe computer, in exchange for becoming reinserted into the Matrix. After Morpheus was captured, Agent Smith and his agents interrogate him in order to reveal the code, but the rebel leader was rescued by the joint operation of Neo and Trinity.
The Machines also have their own mainframe which is heavily defended as their first line of defense.