A predicate noun follows a form of the verb "to be".
He is an idiot. (Here idiot is a predicate noun because it follows is; a form of the verb "be".)
A predicate noun renames the subject of a sentence.
Margaret Thatcher was the Prime Minister. (Margaret Thatcher is the subject and Prime Minister is the predicate noun - notice it follows 'was' the past tense of 'to be'.)