A border router in the PfR world is a router that has an exit interface to an ISP or other attached networks. The border router is where policy decisions from the MC are enforced.
Border routers monitor for prefixes and transit links on behalf of the MC, and report their data to MC for it to be computed and matched against configured policies.
The MC will instruct the border router to alter any packet flows in the network as necessary. Keep in mind that border router processes can be housed within the MC in some setups.