The purpose of this book, On Writing: A Memoir of the Craft by Stephen King, actually splits off into two main purposes: to entertain, and to inform. (though "to inform might" not be the best word... "to propose" would work well...)
I came to this conclusion by reading the top reviews of the novel on Amazon.com. Though one review was nothing but positive, and the other was a tad negative, both reviews voiced clearly the novel's purpose. And having reading it myself, I agree.
As far as entertainment goes, Stephen King is a master in the craft. The first and third sections of the book are autobiographic in nature. King spins tales from his childhood that made me laugh out loud. One being printed on page 54. He was explaining the school paper that he headed while he was in high school, and that he wrote about the teachers. However, he had used the nicknames that the students had given the teachers instead of the teachers' actual names. He got called down the office for just one teacher who wasn't too keen on her nickname being "Maggot Margitan" (this was the only teacher that was not willing to let bygones be bygones). In the end, young Stephen had to give Miss "Maggot" Margitan a formal apology and suffer two weeks of detention. During his detention spell, he deduced that the reason he was in that situation in the first place, was because Miss Margitan just didn't like boys.
In the "to propose" aspect, the middle part of the book was the actual "on writing" portion.
In this section, King tells of all the writing techniques that worked for him and what didn't. He gives lessons on prose and inspiration; in a way, he is proposing that one could try these same techniques, or that others feel the same way while they are writing. He gives suggestions periodically throughout the book on the mechanics of writing (some of which I found to be helpful). One of the suggestions, or proposals, he gives when writing is use adverbs in dialogue attribution, and also that using "he said" or "she said" is perfectly acceptable.