What is REST?
REST is an architectural style for lightweight applications. Please read http://en.wikipedia.org/wiki/Representational_state_transfer for more details.
What support exists for REST application development in the JavaEE world?
REST applications can be developed using JAX-RS.
How do I secure REST applications?
PicketLink can be used to secure JAX-RS applications.
Please take a look at the quickstarts below.
Quickstarts for REST Security
https://github.com/jboss-developer/jboss-picketlink-quickstarts/tree/master/picketlink-authentication-rs-endpoint [Authentication using REST endpoints]
https://github.com/jboss-developer/jboss-picketlink-quickstarts/tree/master/picketlink-authorization-rs-rbac [Quickstart that demonstrates how to use RBAC to your JAX-RS Endpoints]
How does REST security related to Mobile security?
Majority of the Mobile HTML5 applications are REST applications. So they are closely related. Mobile Application Security With PicketLink