JSON-RPC is a standard JSON data-format based (r)emote (p)rocedure (c)all protocol.
See http://json-rpc.org/ for specification and implementations for various languages.
JSON stands for JavaScript Object Notation. It is a text-based lightweight data-interchange format. See http://www.json.org/ for details.
RPC stands for remote procedure call, which is a family of protocols. See the Wikipedia article Remote procedure call for origins, current variations and applications.