Canada contributed to the Allied war effort in a variety of ways, including sending hundreds of thousands of men and women overseas as well as producing vast amounts of material and equipment. I'm going to try and keep this as high-level as I can, since any one of these topics could be a post in and of itself.
Starting with the home front, from the beginning of the war the government of prime minister William Lyon Mackenzie King envisioned Canada playing a significant role -- although not necessarily the role it would actually play. King, remembering the heavy losses that the Canadian Expeditionary Force suffered in western Europe during the First World War, sought a war of "limited liability". The government hoped that by focusing on providing personnel for service in the air force and the navy that the casualties that ground forces experienced in 1914-1918 could be avoided. Furthermore, avoiding the high losses of the First World War would theoretically allow the government to prevent another conscription crisis. As the war proceeded, this vision was increasingly rendered impractical.
To that end, the King government was eager to find ways for Canada to contribute to the war effort without the risk of high casualties. It soon became clear that Britain lacked the resources or the physical space to train the pilots and other personnel necessary to sustain the Royal Air Force (RAF) during wartime. As such, negotiations between Canada and Britain began in September 1939 for Canada to take over the responsibilities for training pilots from around the Commonwealth for service in Britain and beyond. What became the British Commonwealth Air Training Plan (BCATP) trained over 130,000 personnel at 151 schools across the country, serving the needs of the RAF, the Royal Canadian Air Force (RCAF), the Royal Australian Air Force, and the Royal New Zealand Air Force.
Meanwhile, Canadian industry worked alongside the US to meet the vast material needs of the Allied armies. The automotive industry, consisting mostly of "branch plants" of American manufacturers, led the way in terms of its industrial output during the war. While Canadian production of tanks (~50,000) and aircraft (~16,000) was surpassed by other nations, the production of 815,729 transport vehicles for the Allied war effort was significant.
Without getting bogged down in the details, Canadian forces fought in most major theaters of the war. Approximately 2,000 Canadians were dispatched to Hong Kong to defend against a possible Japanese assault. When the assault came in December 1941, "C Force" and the rest of the Allied garrison were quickly overrun. Those who survived the rather one-sided battle faced four grueling years in Japanese POW camps. Canadian troops contributed forces to the Dieppe raid in 1942 and landed in Sicily alongside the British and the Americans and served with distinction throughout the Italian campaign.
The 3rd Canadian Division landed alongside the British and the Americans on D-Day on June 6 1944, on a beach code-named "Juno" that was sandwiched between the two British beaches. In the days and weeks thereafter the division faced hard-fighting and experienced serious losses, although as with the other allied forces they made progress. The 3rd Division was instrumental in closing the gap between the Anglo-Canadian and American fronts in Normandy, which finally met in August 1944 near the town of Falaise, cutting off the remnants of the German Seventh Army. The closing of the "Falaise Gap" is usually considered the final act of the Battle of Normandy. Thereafter the First Canadian Army, made up of 5 Canadian divisions as well as several British and Polish divisions, formed the left flank of the Allied armies in northwest Europe, liberating much of Belgium and Holland and eventually pushing into Germany by the war's end.
Elsewhere, thousands of Canadians served in special squadrons of the Royal Air Force (RAF) or in the Royal Canadian Air Force (RCAF) in both Canada and Europe. Canadian airmen shared in the heavy casualties sustained by Bomber Command throughout the strategic bombing campaign against Nazi Germany, a reality which clashed with the "limited liability" dreams of the King government. 17,101 Canadians lost their lives while serving in the RCAF, a disproportionate rate of loss compared to the other services. The Royal Canadian Navy (RCN) protected Allied convoys that sailed between North America and Britain carrying the food, munitions, and supplies that kept the war effort alive. The Battle of the Atlantic, wherein the Allies withheld German efforts to cripple their supply lines via submarine warfare was the major preoccupation of the RCN during the war.
Despite these contributions, Canada did not have a major part to play in allied grand strategy. If King and his cabinet had different ideas of how the war should have been fought, they kept it well under-wraps. Beyond lobbying the British government and Imperial General Staff regarding the use and deployment of Canadian personnel, Canada had a minimal voice in the conduct of the war. As Desmond Morton put it, King was content to be photographed alongside Roosevelt and Churchill while they did the strategic heavy-lifting -- a slightly unfair assessment, I think, since the odds are that any input King provided would have been politely ignored.
During the course of the war, 1,086,343 men and women served in the army, navy, and air force in one capacity or another; a significant sum for a nation with a population of approximately 11 million in 1939. Of this number, 96,456 became casualties. By the war's end the RCAF was the world's fourth-largest air force and the RCN was its third-largest navy, remarkable achievements for a country with minimal forces in each respect prior to the start of the war.
TL;DR (which I would understand): Canada made important contributions in terms of manpower and material to the Allied cause.
Edit: some formatting
Sources:
Stacey, C.P. Arms, Men, and Governments: The War Policies of Canada, 1939-1945 (1970)
Stacey, C.P. The Victory Campaign: The Operations in Northwest Europe, 1944-1945 (1960)
Morton, Desmond. A Short History of Canada, Fifth Edition (2001)
Veteran's Affairs Canada, "Canada Production of War Materials"