These are the misfits, the intellectuals, those who do not belong; they are reminiscent of the outcases in "Brave New World" who can not or will not adapt to the society they find themselves in. Their major function in the book is simple: each of them has memorized a famous book so that the information/philosophy it contains will remain even after all the books have been "burned" in the attempt to create a more stable society. It's almost a reversal to the pre-writing times when "books" were passed on by word of mouth, not by reading.
At the end of the book it appears that their services are in demand as they return to civilization ....
Their total purpose is to keep the book or books they have memorized from being lost to the fire of censorship. They create the story within themselves and ultimately become that piece of literature. Once memorized they recite it constantly to themselves and others in the wilderness. If one can identify with and become part of a "work" it can never be erased or destroyed. They function as living Libraries far from a world gone mad hoping to, perhaps, oneday surface and renew their beloved classics to a sane world.