An edge server, in a system administration context, is any server that resides on the "edge" between two networks, typically a private network and the Internet. Edge servers can serve different purposes depending on the context of the functionality in question.
- Security Context: usually a firewall, router or similar device
- Application Context: a web load balancing server
- Mail Context: some kind of hub server that forwards mail on to internal servers
Usually an edge server has some kind of gateway responsibility for the internal/private network.
Snipped from serverfault.