Bears are "ursine" creatures, distantly related to dogs and canines, but larger and more muscular. For factual information about real-world bears consult Wikipedia.
Bears in D&D are classically ferocious, highly damaging, wild brutes. They dwell in many colder habitats, and are often domesticated by various people that reside in those habitats. They are special to barbarians, shamans, and other tribal folk as spirit animals.
Bears share several traits in common:
Bears attack by mauling, attacking with their claws and hoping to knock thier prey to the ground. They are frequently well-camouflaged in their home environments, and attack with surprising speed, intelligence, and patietice, as well as their overwhelming strength.
Bears are genuinely interested in two main things: food and mating. Provide one or the other, and you can shape the bear's behavior to your whim.
Bears follow those that provide them food. In the wild, the biggest and strongest bear often commands the most respect, gaining prime feeding grounds and access to the best mates (who will frequently look for food in their territory).
Bears are omnivorous, by and large. Some bears -- such as pandas -- are entirely herbivorous, and others -- like dire bears and cave bears -- are entirely (or nearly so) carnivorous. They dwell mainly in the colder areas of the world, though warmer regions certainly may have their native species.
Black bears are the smallest and weakest of the bears here, though they are still quite powerful. Brown bears (including the dangerous grizzly bear) are next. Polar bears are the hardiest "natural" bears, the largest and most powerful. Dire bears eclipse them all, and are the size of a small house.
Werebears are lycanthropic bear-people with the ability to shift between human and bear form. They tend to be benevolent, though individualistic.