Hafiz

In the introduction of the text on the Qur’an we are currently reading it mentions that someone who memorizes all the parts of the Qur’an is considered a Hafiz. It goes on to say that this has been an occurance since the days of the Prophet Muhammad. I am confused by this because I don’t understand if this means they memorized all of the chapters of the Qur’an. Or if they loosely know all the lessons that are taught in the Qur’an. Or if this means that they literally memorized the Qu’ran word for word. In that case are these individuals equivalent to monks? I just don’t see how someone could memorize all of these words. This book is over 400 pages.