A proxy acts as an intermediary for requests from clients seeking resources from other sources they don't have direct access to. When you encounter this term in relation to Android, this is mostly used for connections to the internet.
Quoting Wikipedia:
In computer networks, a proxy server is a server (a computer system or an application) that acts as an intermediary for requests from clients seeking resources from other servers. A client connects to the proxy server, requesting some service, such as a file, connection, web page, or other resource available from a different server and the proxy server evaluates the request as a way to simplify and control its complexity. Today, most proxies are web proxies, facilitating access to content on the World Wide Web.
For visualization, here's an image from the very same Wikipedia article:
Communication between two computers (shown in grey) connected through a third computer (shown in red) acting as a proxy.
