The application model in CouchTalk assumes sequential keys, allowing for efficient indexing of data without issuing queries. The app uses a combination of HTTP servers and PubNub to manage real-time communication between clients and the server. The use of an INCR key pattern enables atomic increment operations, ensuring that there are no collisions when generating keys. This approach allows for efficient management of related data in Couchbase Server, making it suitable for applications with high performance requirements such as push-to-talk messaging.