If I'd have to vote for the most important HTML5 new API, I'd select WebSockets. This is a new protocol that allows full duplex communication as opposed to request-response HTTP model. WebSockets API is included in the Java EE 7 (JSR 356).
HTML5 specification includes WebSockets, a new communication protocol for the Web. It's becoming the best choice for building real-time Web applications. This presentation is an overview of the servers and frameworks that support WebSockets. You'll see some use cases where WebSockets shine. We'll also discuss various approaches for the server- and client-side implementations of WebSockets that can be used in the Web applications today.
Example application could be found on github