I am new to Adobe InDesign CS6 and are exploring the features. It is possible to create a template, then use it for a while and then update the template again and let the new update of the template be adapted to the current pages that already uses the template?
No. Templates are a one-direction mechanism.
You start from the template and then the template is no longer referenced. In other words, templates are only referenced when a new file is opened. They aren't "linked" to anything after that. Making changes to a template after the fact does nothing to alter any files previously started with that template.
That being posted, you can utilize things like object styles, paragraph styles, character styles, and the Library to store commonly used items.
By the way, this would be a great feature to have... something like Global styles that are always referenced or linked to documents. Similar to how linked images function.
EDIT: It did just occur to me that if you use the Book command and all your files are merely chapters in the book, you do essentially get global styles. Any alteration to the book styles would be reflected in all chapter documents. Whether or not it is feasible to use the Book command for everything may be another matter though.
I'm also not clear about the question since you specifically mention "pages". If you mean you have different pages in one document, you can utilize master pages to configure a common template or theme for pages in that document. Altering a master pages does update any page which references that master, but again, only in that InDesign file. If you mean "pages" as in separate InDesign documents... then everything else in this answer applies.