EIGRP is a proprietary routing protocol developed by Cisco that uses a composite metric and has fast convergence properties. It functions as a hybrid of distance-vector and link-state routing protocols, sending subnet mask and VLSM information in updates. EIGRP forms neighbor relationships through periodic hello messages and establishes three key tables - Neighbor, Topology, and Routing - to store neighbor, route, and best path information. It utilizes five packet types and reliable transport to efficiently share routing updates.