Daily is a video and audio API that allows developers to build real-time video calls into their applications. Daily's APIs are frontend framework-agnostic, making it easy for developers to integrate with various frameworks such as React and Vue.js. The demo app built using Daily's call object mode provides a custom video call experience with features like screen sharing, chat, and device permissions management. The app is built using Vue.js and uses Daily's JavaScript API to handle the video and audio aspects of the call. The demo showcases how developers can create a custom UI for their video or audio-only apps using Daily's APIs.