Explain types router core types: high-potential?

Types of core  routers depends on the brand.

However, usually for Cisco there are three types of routers:

a. Branch Office

b. Network Edge/Head Office:  Cisco ASR1000 Series Aggregation RTR

c. Service Provider:

 Cisco ASR1000 Series Aggregation RTR, Cisco ASR9000 Series Aggregation RTR,Cisco7600 Series Router, Cisco XR12000/12000 Series Router,ASR903 Series Aggregation Router.

To see details about these please check the following link:

http://www.cisco.com/en/US/products/hw/routers/index.html

A core router is a router that forwards packets to computer hosts within a network