July 1st is Dominion Day or what is now called Canada Day and it celebrates the formation of Canada as a nation comprising a union of Ontario (Canada west), Quebec (Canada East), Nova Scotia and New Brunswick. This was declared by the British North America Act of July 1, 1867 and is known as a Confederation. After that Canada started to acquire more lands to grow to what you see today. Sorta like your 13 States that initially were the union and then all the rest came aboard later as the nation grew and settled west.
We are members of the Commonwealth of Nations and Her Majesty Queen Elizabeth II is our official head of state. We are an independent, self-governing democracy as you are but our form of government is a constitutional monarchy, whereas I guess you are a republic. In reality the Queen has no part to play in day to day government and only appoints our Governor General who is the Queen's representative and even that is done based on the government of the day's advice.
Our GG plays largely a symbolic role as well. So you can see why some people wonder why in the heck we hang onto the Queen at all! Old school, feels good, great pageantry, 2 major wars fought under the Union Jack or Red Ensign, a grand confederation to belong to...all contribute to the attachment to Britain. Australia is the same as we are and from time to time we hear rumblings from down under that maybe they will make a break from a constitutional monarchy and go the republic route. So far we hang on but i can foresee the day when the numbers of immigrants grows so large that old traditions will not be so impt. and we may move away from this form of gov't. The English majority I think is already a thing of the past.
Hope this helps ya!