Essentially, because the provinces, which in general were originally much smaller (encompassing the populated areas), had large sections of hinterland glued onto them.
Most of the northern regions of the provinces other than the Atlantic provinces were originally part of the immense regions of Rupert’s Land (the Hudson Bay watershed) and the North-Western Territory (the Arctic Ocean watershed). The colonies of Upper and Lower Canada, the embryos of modern-day Ontario and Quebec (merged into one Province of Canada in 1841), consisted of the St. Lawrence River and Great Lakes basins. Similarly, the colony of British Columbia only extended as far north as the Simpson River.
In 1862, what is now northern BC was detached from the North-Western Territory as the Stikine Territory, and became part of BC a year later, in response to the Gold rush.
In 1867, the provinces of Canada, New Brunswick, and Nova Scotia formed the Dominion of Canada, with the Province of Canada splitting back into Ontario and Quebec. Three years later, Rupert’s Land and the North-Western Territory were ceded to Canada as the North-West Territories; at the same time, a small square area around Fort Garry (modern Winnipeg) became the Province of Manitoba. BC joined in 1871, and the rest of the Arctic Islands (until then retained by the UK) were ceded to Canada in 1880. Yukon was created in 1898.
The most populated parts of the Northwest Territories were erected as provinces in 1905: Alberta and Saskatchewan. The Northwest Territories had been governed from Regina, but as this was now in Saskatchewan, the territory was henceforth governed from Ottawa.
Finally, in 1912, the remaining parts of the Northwest Territories north of Manitoba, Ontario, and Quebec (which had been slowly expanding in the meantime) were transferred to those provinces.
In other words, the provinces, which had started out as fairly densely populated regions gradually accreted very sparsely populated areas that had been part of the Northwest Territories.
Fun fact: following redistricting in Western Australia, the federal riding of Nunavut is now the largest single-member electoral constituency in the world.