Generally a network service that is in between two other hosts (or two ends of a logical connection). It forwards traffic between them, and is often used as a place where filtering or traffic inspection/manipulation takes place. Think caching server, network filtering, security, etc.

What is the difference between a forward proxy and a reverse proxy?

Forward proxy: on the client’s side of the network — usually used for caching or filtering traffic.

Reverse proxy: usually on the server’s side of the network — e.g. proxying traffic for a large pool of application servers.