In today's usage the term can refer to any type of bear, but is probably used in reference to sports teams far more often than actual animals -- most notably the UCLA Bruins and the Boston Bruins of the National Hockey League.
Why Bruins?The bear has been a symbol of California dating back to the 1840s, when it was used on the flag of the California republic. As such, two of California's biggest state universities use bears as mascots -- the UCLA Bruin, and the Cal Bear.
Belmont University in Nashville, Tennessee also calls its sports teams The Bruins. But the UCLA version has more championships, so he gets his picture on this page.