A huge, shallow bay in north central Canada, joined to the Arctic ocean in the north and the Atlantic ocean in the north-east, with Baffin Island in between. The bay is part of the drainage system for not only the Canadian provinces of Québec, Ontario, Manitoba, Saskatchewan, Alberta, and the Canadian territory of Nunavut, but also the states of North Dakota and Minnesota, which drain north into Manitoba.
The bay was originally thought to be part of a north-west passage to Asia, many explorers tried to failed and failed to navigate it. The bay is named after one of these, Henry Hudson, who was set adrift in the bay after a harsh, frozen winter by his mutinous crew, and was never seen again.
Despite its failure as the north-west passage, the bay provided access to Canada's interior for the fur trade of the 1600s and 1700s, establishing the success of the Hudson's Bay Company. (The bay was formerly "Hudson's Bay" but is now styled "Hudson Bay". Apparently even geography has fashions!)