The boat now sold in plastic at every outdoor store was designed for hunting seals, and its name has barely changed since.
The word is Inuit. Etymonline traces English kayak to Danish kajak, which came from Greenlandic qayaq, literally "small boat of skins." Wikipedia gives the Inuktitut form as qajaq and the Yup'ik form as qayaq. It links the Yup'ik word to qai-, "surface" or "top." Wikipedia also gives the popular glosses "man's boat" or "hunter's boat," but Etymonline does not, so treat them as informal.
English first recorded the word in 1757, according to Etymonline, as the name of a light boat made of sealskins stretched over a wooden frame. The verb, to kayak, came much later, in 1875.
The design was built for the Arctic. The Canadian Encyclopedia describes a one-person, closed-deck hunting craft, four to seven metres long. Hunters stretched de-haired seal or caribou hide over a frame, often driftwood with willow ribs. The paddler wore a parka tied around the rim of the hatch-hole.
Materials depended on what the land offered. Wikipedia notes that peoples of western Alaska framed their kayaks in wood. Eastern Inuit, living in treeless country, used whalebone. From the Aleutian Islands to Greenland, the boats were used mainly to hunt seals, and in some places whales and caribou.
The kayak had a larger cousin. The umiak, from Inuit umiaq, was an open skin boat carrying 10 or 12 people. Etymonline notes that 18th- and 19th-century sources called it a "woman's boat," in contrast to the kayak, which was paddled by men.
How old is the kayak? Sources differ. The Canadian Encyclopedia says Inuit have used kayaks for over 2,000 years, while Wikipedia says they are believed to be at least 4,000 years old. The oldest surviving examples, held at a museum in Munich, date from 1577.
The leap to Europe came in 1860, when, according to Wikipedia, John MacGregor introduced a kayak-style boat to England and Europe. Kayak sprint racing reached the Olympics in 1936. Few Arctic communities still hunt from kayaks today.