Proxy Server
A proxy server is a server that stands between two network devices, a client and a sender. The client sends a request to the proxy, which then forwards it to a target server. The target server responds to the proxy, which then responds to the client on behalf of the target. The target server never sees the IP of the client. There are several applications and purposes for proxy servers, most notably including reverse proxies.
Reverse Proxies
In a reverse proxy, the proxy faces a web server on its own network. The web server isn't accessible from the internet, but the proxy is, potentially through port forwarding. An internet user sends a request for information to the proxy server, and the proxy server then relays that to the web server. The web server returns the information back to the proxy, which then returns it to the internet. The important detail here is that the reverse proxy can accept or reject requests depending on certain criteria. This adds a helpful point in which to add authorization measures, such as Authelia.