Hmmm...  Those are all very basic concepts that are shared among nearly all forums on the Internet.  I am not sure about documentation explaining these concepts, but I will attempt it for you.

Thread - the single instance of a discussion consisting of an initial post, and one or more replies.  Use this when you want to begin a new topic. 

Reply - a single post replying to an existing thread.

People use quotes to show that they are replying to a specific statement or post in the thread.  When to use it is up to you.