The Daily Custom Session Data Feature allows participants to share client-side state scoped to a video session with other participants. This feature enables custom data sharing between participants in a video call, making it possible to pass information such as jokes or other shared content between participants. The feature can be used to enhance the functionality of video conferencing applications by allowing users to share and interact with each other's content in real-time. The code provided demonstrates how to set up this feature using Daily's JavaScript API, including setting custom session data, responding to "meeting-session-state-updated" events, and retrieving meeting session state on demand.