Demian, like several other books by Hesse, is a book about the growth of an individual, in this case Emil Sinclair.
Emil Sinclair's life is an ordinary one: he is an ordinary adolescent growing up in an ordinary household, encountering ordinary troubles and coming up with ordinary and ineffective solutions to these problems. Into this world enters someone who is not ordinary, who does not live in an ordinary household and who does not seem to have any of the ordinary problems. This someone, Demian, solves Sinclair's inconsequential problems quite easily.
He takes Sinclair under his wing and shows him that what distingishes between ordinary and extraordinary is simply thought and action based on a deep rooted understanding of human nature. This knowledge is enough to alleviate many of the troubles which afflict most people, allowing more time for higher pursuits, for growth.
Demian guides and helps Sinclair during the early stages of his development. Sinclair's growth is incidental - he takes to Demian because Demian solves his problems. Ultimately he must move away. If he is to continue growing significantly however, there must ultimately be an awareness and a desire for it. Growth must eventually come alone and will only come if there is a strong and persistent hunger for it.
Demian is a good teacher, but like most teachers he fails because of his zeal to educate. For higher education to be successful, the student must seek out the teacher. If the teacher has to seek out the student, the student is probably not yet ready to learn. Moreover, the teacher in seeking out a student halts his own growth.
In Demian, as in many of his books, Hesse suggests a philosophy which stresses that an essential requirement for mental fulfillment is an awareness of what is required for fulfillment. This awareness in turn leads ultimately to the realization that the road to fulfillment is a lonely one.