Core groups were introduced in WebSphere Application Server Network Deployment V6.0, and my impression is that they are still not well understood by customers. Part of the reason why is that, by default, a single core group is created for the entire cell and all new servers are added to that core group, which means users can go quite awhile without ever needing to know anything about the core group concept. It's not until you try to create large-scale topologies that core groups become a critical component in the configuration. The one sentence definition of a core group is that they are a group of processes that talk to each other to maintain knowledge about each other's state for purposes of failover/HA.
But what about a core group bridge? A core group bridge is a communication vehicle between multiple core groups, either within a cell or between cells. One interesting scenario where a core group bridge is handy is when you have a cell for your proxy server in a DMZ and a cell for your application servers on the other side of the firewall. You want your proxy server to know about the state of the application servers for obvious routing purposes. How do you do this? Via a core group bridge.
I've been trying to learn more about core groups recently and a colleague pointed me to a good article on developerWorks that provides a good introduction to core group bridges entitled Core group bridges 101. I highly recommend it for anyone working with large topologies or trying to create communication between cells.