Plain English Meaning
A way for controllers and pilots to send each other typed messages instead of talking on the radio. FANS 1/A is the message format, and VDL Mode 4 is the radio channel that carries those messages.
Full Definition
A specific implementation of text-based controller-pilot messaging that uses the FANS 1/A protocol (the message standard developed by Boeing and Airbus for oceanic and remote operations) carried over VDL Mode 4, a VHF digital data link that exchanges short messages between aircraft and ground stations on VHF frequencies. Together they let a controller send clearances, instructions, and information to the cockpit as text messages, and let the pilot respond, without using voice radio.