A doctype or document type declaration is an instruction which tells the web browser about the markup language in which the current page is written. The Doctype is not an element or tag, it lets the browser know about the version of or standard of HTML or any other markup language that is being used in the document.
A DOCTYPE is always associated to a DTD - for Document Type Definition. A DTD defines how documents of a certain type should be structured (i.e. a button can contain a span but not a div)