In real life, handshaking is the act of gently grasping two people's hands, followed by a brief up and down movement. If you have ever greeted someone this way, then you already understand the basic concept of the HTML5 WebSocket protocol.
WebSockets define a persistent two-way communication between web servers and web clients, meaning that both parties can exchange message data at the same time. WebSockets introduce true concurrency, they are optimized for high performance, and result in much more responsive and rich web applications.
The following diagram shows a server handshake with multiple clients:
For the record, the WebSocket protocol has been standardized by the Internet Engineering Task Force (IETF) and the WebSocket API for web browsers is currently being standardized by the World Wide Web Consortium (W3C)—yes, it's a work in progress. No, you do not need to worry about enormous changes, as the current specification has been published as "proposed standard".