Imagine that you’ve got a friend who’s in some technological backwater where he can only read email, and he wants to hear all about these books, and insists that after you finish each chapter, you send him a short summary. What do you tell him about each chapter?
(This technique works incredibly well for writing at all levels—I never actually motivated myself to write my masters’ thesis directly, but instead wrote a lot of emails to my friends about what the next chapter was going to be—emails that I never actually sent, but edited into the thesis.)
Also, my French Composition teacher was very fond of making people write a précis for passages from the writings we studied: the précis has to have 10% of the words of the original text, plus or minus 10 words, and all of the important points have to be mentioned. This is a very difficult exercise, but you learn a great deal from it. Maybe this is the sort of thing your teacher is aiming at, but in a less rigorous way?
(My teacher was completely rigorous about the requirements—if she assigned a précis of a 500-word passage, and you turned in something with fewer than 40 words or more than 60 words, you failed the exercise. The word count was an absolute requirement.)