Face-to-face interaction was the social interaction of people who were in the same room, or facing each other on a viewscreen, as opposed to letters.
In 2266, Commander Spock and Lieutenant Stiles agreed that the USS Enterprise should attack a Romulan Bird-of-Prey which was on the Earth side of the Romulan Neutral Zone. Doctor Leonard McCoy was dismissive of attacking them based on the memories of a war over a century before, and on theories about people they had never met face-to-face. (TOS: "Balance of Terror")
In 2364, Lieutenant Commander Dexter Remmick asked Commander William T. Riker about discrepancies in the Captain's log; if Jean-Luc Picard ever falsified a log. Riker told Remmick to bring Captain Picard into the ready room and ask him face-to-face if he wanted to discuss anything about Captain Picard. (TNG: "Coming of Age")
In 2366, Lieutenant Commander Data volunteered himself as a conduit for a face-to-face negotiation with nanites who had infested the USS Enterprise-D. (TNG: "Evolution")