Q:

What is an edge server / router / device?

What is an edge server? We see some references to them, but we never see a definition.

A:

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.
Some examples:

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.

A:

It's usually a caching proxy server, located near the user accessing the data, used to improve bandwidth and latency to far away users while lessening the load on central servers.
http://en.wikipedia.org/wiki/Content_delivery_network

A:

By EDGE do you mean Enhanced Data GSM Environment? It pretty much stores data files on remote servers with the specific purpose of streaming them over the internet.
Edge Server – (Enhanced Data GSM Environment) Storage of data files on remote servers specifically designed for streaming over the Internet. EDGE is a faster version of GSM wireless service. EDGE enables data to be delivered at rates up to 384 Kbps on a broadband. The standard is based on the GSM standard and uses TDMA multiplexing technology. Source

