The Intermediate reader is expected to be rather well-versed in the whole Harry Potter storyline. Much of the plot is known to the reader and he/she wishes to expand on that with analysis and commentary. Most of the character pages and sections are open. In addition, Intermediate readers have access to chapter summaries for referencing specific details.
Not much is kept from the Intermediate reader. Most major content is covered - filling in the gaps is all that is left. An Intermediate reader should feel knowledgeable about the topics covered in the books, but perhaps not quite grasping the full importance of scenes and character actions, referred to as the Greater Picture which is excluded until the reading of the series can be finished.
Once the reader has completed the entire Harry Potter series, the next step is the Advanced level. The Advanced level details the entire storyline. Advanced readers have access to the Greater Picture section seen on many pages - it connects all the pieces together.