It's all because a US president decided not to shoot one when he went hunting way back in 1902.
The 26th president of America, Theodore 'Teddy' Roosevelt, couldn't find a bear to shoot when out hunting, but refused to shoot one that had been tied to pole just for him.
The name came from a cartoon
A political cartoonist heard about it and drew a cartoon with a cute bear in it, which gave toy companies the idea to start making stuffed fluffy bears, that they called Teddy's bears.
Over the years the stuffed bears have become teddy bears, and in America there is a special exhibition being held to celebrate them.