They're something Fizzer implemented in a recent update. Go to settings (Ctrl+F "sockets" to find the option) and enable them. Basically, they allow you to connect directly to the server so you don't have to send a request every 10 seconds or press the Refresh button anymore (in games).
If you're wondering what exactly a "socket" is (outside the context of just Warlight): it's basically an endpoint for two-way communication (in this case, between your client and the server)- think of it like one end of a phone call. For a better explanation, it's one of the few things the Oracle Java Documentation doesn't suck at explaining: https://docs.oracle.com/javase/tutorial/networking/sockets/definition.html
As you can see by looking (briefly) at the Python socket library (https://docs.python.org/2/library/socket.html
), if you're working with them directly you're probably doing low-level networking.
In the context of Warlight, then, the new sockets feature just lets you set up a direct (or semi-direct, not sure exactly what's going on in the backend) connection between your client and the server, kind of like what you'd have on a proper chat server that updates instantly.
Edited 7/15/2015 05:31:54