The BNA act outlined the responsibilities of each level of government.
Education was included as a provincial responsibility because of the recognition of special language and religious rights of people in different parts of the country.
The BNA act only identified powers for two levels of government so the provinces delegated some of their powers to municipalities. This provided communities with more control and flexibility over issues of local importance.
You can see further provincial responsibilities listed here under section 92:
http://laws-lois.justice.gc.ca/eng/const/page-4.html#h-18Federal and provincial divisions of power are also listed on page 67 of the text.