In computing, a proxy is typically a server, and it is a server that acts as a middleman between a client and another server. It literally is a bit of code that sits between client and server. That's the crux of proxies.
If there is a middleman server that receive requests , then sent them to another service, then forwards the response it got from that other service back to the originator client, it would be a PROXY SERVER.
So when a client sends a request to a server via the proxy, the proxy may sometimes mask the identity of the client - to the server, the IP address that comes through in the request may be the proxy and not the originating client.
Forward Proxy versus Reverse Proxy
A forward proxy is one where the proxy acts on behalf of (substitute for) the client in the interaction between client and server.
A reverse proxy is designed substitute for the server. Often clients won't even know that the network request got routed through a proxy and the proxy passed it on to the intended server (and did the same thing with the server's response).