They are based off the berserkers, light infantry troops the germanic tribes had. The etymology of their name is supposed to either come from "bear", although this is disputed, as fur is heavy.
More likely it was formed out of the word "bar" today in German a prefix meaning no clothes. Very comparable to the English "bare", as in "bare-naked".
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They appear in nordic folkore as well around the 9th century, where they are often described as wearing wolf-fur and fighting without consideration of their personal well-being. They are also said to fight without body armour. However outside of folklore there are little sources on their actual use and/or equipment. So there is your reference.
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Just like with many things in Bannerlord it is a not a mirror of our medieval times, but with added flavour drawn from sagas, their own lore and pop-culture.