Proxies are a dedicated server, which handles connections between back end servers.
Backend Servers are multiple servers running separately. Using Minecraft as an example, these backend servers are separate servers, like a lobby, survival server, etc.
The proxy handles these connections. So a client (a user), will connect to the proxy, and then the proxy can decide what backend server they will redirect the user to. and when ever they are connected to a backend server, the proxy can interrupt the connection, and force them to switch servers.
Proxies are extremely useful if you know what you are doing. Likewise, using Minecraft as an example, if a user is playing on the Survival server, and somehow the server crashes, the proxy can detect that there are no packets being sent to that server, which triggers the proxy to send users to the lobby. This means that if one server on your network crashes, all the other servers will still stay online.
This also allows for you to separate what's on each server. If you had just one single server without a proxy, all your plugins will be duplicate across servers (If you are using multiverse), this is not ideal, as you may be able to access commands you only want available in one server, to be executed in another. This is where proxies allow you to put plugins on different servers, as in simple, you are just creating an entire new server for different use cases.