The Twilio Video API allows developers to create high-quality peer-to-peer video conversations in the browser, using standard WebRTC technologies. The API provides a rich set of features, including server-side control over conversations, intelligent management of client-side experience, and cross-platform use of APIs like WebRTC's data channel. To get started with Twilio Video, developers need to create an account, install Node.js on their system, and access the video beta program. They also need a web browser that supports WebRTC, such as recent Chrome and Firefox builds. The API provides a JavaScript SDK that can be used to build a communication experience in the browser. The server-side code generates a secure keypair using Twilio's REST API, which is then used to sign an access token for the client. This token grants limited permissions to use Twilio back-end services for NAT traversal and general "endpoint" services like listening for inbound calls and initiating outbound calls. With this setup, developers can create basic video calling applications with two parties in the browser, as well as a backend to handle generating capability tokens using their Twilio account.