CEF, or Cisco Express Forwarding, is a layer 3 switching technology. It’s an improvement over fast switching and route processor switching.
The FIB, or Forwarding Information Base, is a direct copy of the routing table. If a change occurs on the routing table, it is also reflected in the FIB.
CEF and FIB are a team. Together they are fast. CEF is known as a topology-based switching operation, hence the FIB. Because the information CEF uses is stored in cache, it is able to switch subsequent traffic flows much faster.
References: Understanding Cisco Express Forwarding (CEF)