"rendered" means that a graphic element is drawn on the resulting webpage. If you set "rendered=false" on an element, that element (and its childred) will not be displayed.
"updated" isn't actually a formal JSF term, but all it means usually is that the web page is re-drawn. AJAX uses a concept known as "partial page updating" to redraw only a section of the page without erasing and redrawing the whole page.
When a page (or page parts) is updated, the rendered= values for the elements being updated will be applied according to their current values. So you can use a partial page update to show and hide a section of a page.
An IDE is no substitute for an Intelligent Developer.