Canada Day (formerly Dominion Day) has not really been on the radar of most Americans, i think. I'm not saying nobody knows, just that, as usual, the Americans don't pay much attention to what goes on north of the border.
At the time of the American Revolution, "Canada" was two North American provinces, Lower Canada (Québec) and Upper Canada (Ontario). At the time, Upper Canada consisted of little more than Fort Henry and the nearby village of Kingston, and some scattered farmsteads along or near the shores of Lake Erie. Loyalist from the United Stares, known as Tories there, and calling themselves United Empire Loyalists flooded into Upper Canada after the Revolution. (One sees Loyalist this and that all over southeast Ontario. There is a Loyalist High School in Kingston; i don't recall if The Girl attended that school or not.)
During the War of 1812, about which Canadians have many unrealistic historical myths, Isaac Brock invaded Michigan from Upper Canada, and a superannuated veteran of the Revolution, General Hull, surrendered Fort Detroit to inferior forces. There was a notorious slaughter of prisoners by Brock's Indian allies, lead by Tecumseh who claimed he was unable to control them. Later, the Americans riposted with an invasion of Upper Canada from the west, and soundly defeated the Brits at the Battle of the Thames near present day London, Ontario. Tecumseh was killed in that battle. You find Brock this and that and Tecumseh this and that all over southwest Ontario, including the town of Tecumseh. Brock had been obliged to hurry across southern Upper Canada because of a threatened American invasion, and he was killed at Queenston on the day the Americans invaded.
After the war, the Brits imposed the hated governor and council system of colonial government which was a major factor in American discontent before the Revolution. Finally, in the mid-1830s, there were insurrections in both Upper and Lower Canada because of dissatisfaction in the Canadian provinces with the governor and council system. The Lieutenant Governor, John Colborne, did much to expand settlement and infrastructure in Upper Canada, but he lives on in the resentments of les habitants
as "Le Vieux Brûlot" (the Old Firebrand) because of the burning of farmsteads in Lower Canada, as well as lynchings and outright murders of French-speaking Canadians. Colborne, like Tecumseh at Detroit, disavowed responsibility by saying he had been unable to control the English-speaking militia he had marched in there. The excuse is more feeble coming from a Major General who was a veteran of the Wars of the French Revolution and the Napoleonic Wars.
Retaining the governor and council system had been a pig-headed example of government's inability to admit having been wrong. However, cooler heads prevailed in London, and the two provinces were turned into Canada East and Canada West, and were given a legislature with equal representation for both provinces. Canada as we think of it, though, simply did not exist. Nova Scotia, New Brunswick, Prince Edward Island, Newfoundland and Labrador were all North American provinces separate from the two Canadas.
In 1866, Irish Fenians, veterans of the American civil war, invaded Canada. Most of the "invasions" were farcical, but in the Niagara Peninsula, John O'Neill, a former Federal cavalry officer, lead a successful invasion, and at the battle of Ridgeway, routed the Canadians who had come to round them up. He then retired on Fort Erie, retaking it from the Canadians, and then surrendering to the U.S. Navy in the Niagara River. This was the first "all Canadian" battle in their history, and they have made many cosmetic changes in their record of the event to try to overcome the fact that 300 or fewer Irishmen routed their troops. The British then told the Canadians that they'd have to foot the bill for their own defense and the Militia Act was passed.
At that time, the Tories in Canada West were finding it increasingly difficult to form and maintain governments with their French-speaking partners. The government fell in 1864, but the parties involved began discussions to gain a measure of independence. When John A. MacDonald and George-Étienne Cartier approached a meeting of Maritime provincial politicians in Charlottetown, Prince Edward Island, a deal was worked out which turned Canada East, Canada West, Nova Scotia, New Brunswick and Prince Edward Island into the Dominion of Canada. Newfoundland and Labrador did not join until 1949. The other components of modern Canada had been added in the late 1860s and early 1870s.
As Walter has pointed out, Canada effectively became an independent nation in 1931, when they stopped allowing Parliament to write their foreign policy, and began opening embassies in other nations, beginning with the United States. After 1949, Parliament surrendered the right to legislate the Canadian Constitution. The British North America Act was "patriated" to Canada in 1982.