Definitions
Time to stop an look at a couple of definitions
Servlet Container - A web application that runs in a web server and acts as the Controller for Java web applications.
Faces Servlet - A special servlet that processes JSP pages with JSF tags. (Like its cousin the JSP servlet, JSF compiles pages into a servlet and executes the servlet. These compilers take care of the tedious printlin("<HTML>") command that made sevrlet programming a chore.)
JSF UI Components - Server Side components (Properties, Events and Methods) that encapsulate much of the logic needed to present data to users or retrieve data from users. OutputText and InputText are examples.
JSF Taglibs - Standard tag libraries - A) core and B) html.
Component Tree - When a page is accessed, the first thing the Faces Servlet does is create a tree of the components that make up that page. This tree is saved either on the server or it is embedded in hidden fields as part of the client response. When the next request comes in the tree is rebuilt.