All computers with an IP stack have a loopback interface, which is a virtual interface as opposed to a physical port. In a router, this interface can be allocated an IP address. As the loopback interface is a virtual interface, and not a physical interface, it is always up/available as long as the software is. This characteristic has a number of uses/benefits:

• To use as a Router identifier
• To use as a reachable address as long as one of the physical interfaces is up, and therefore a better way of validating a router is operational than testing any specific physical interface which might be down.
• As an address for a routing protocol adjacency, that maintains an adjacency, and prevents additional routing protocol activity, when a physical interface goes down.
• As an address for unnumbered interfaces.

Further reading:

• Understanding the Loopback Interface, Juniper Networks
• Loopback Interfaces, Cisco Systems
• Cisco Loopback Interfaces Tutorial, Flackbox