In the Couchbase LIVE New York session, the implementation of a peer-to-peer syncing feature using Couchbase Lite was demonstrated through a photo-sharing application called P2P PhotoDrop. This application allows seamless exchange of pictures between devices by generating a sync URL for database connections and employing QR codes to authenticate and initiate transfers. The process involves setting up listeners, observing database changes, creating documents for each photo, and replicating documents between devices. Authentication is secured by generating unique username and password combinations, and the overall code structure remains concise, focusing on core functionalities without directly handling network communications.