Ancestry.ca, the largest online family history resource, can help you explore birth records for Mary Arbie from among its billions of historical records from Canada and around the world.
When a birth is registered a certificate is filled out and given to the person who reported it. The registration information is kept on file and added to the summary register, or Index, of all the events. As in books, the Indexes won't tell you everything, but will give you key information, such as names, dates (specifically quarters) and places (the district the event occurred).
Ancestry.ca has at least 4 birth records for Mary Arbie, among more than 18 birth records for this surname.