The bear paw is used in many different things...
1) Is is a shell native in the West Indies
2) Is is a type of snowshoe (in Canada)
3) Some people also call it a Bear Claw- which is a type of pastry
3) In native art it sybolizes a connection with the bear, or spirit of the bear (spirit bear, grizzly bear, black bear etc) the bear showed gentleness, but could also be fierce. All in all, the bear was a magnificent creature that they respected. They knew a mother bear would fight to protect her cubs, just like any mother would do. She could also be gentle and quiet, however, and she was just as good a hunter as the Indians. The brown bear stands for courage, strength, protection and life.
The spirit bear is an all-white bear known as Kermode Bear. However, for the Native American culture, the Kermode bear is known as the Spirit Bear.(I'm from BC, which is where this bear is native)
According to one of many Native American stories, the spirit bear was made white by the creator of the universe to remind its people the past period of time known as the ice age. It was said that the creator did this to remind the native people of the previous hardship living in all the snow and ice. In addition, in some tribes, the white spirit bear stands for harmony and peace.
The Grizzly bear is often found in Indian paintings and engraved in jewelry, the grizzly was a sign of strength. Native American Indians regarded the grizzly bear with awe and respect. Early hunting tribes noticed that these bears had very complex behaviors. Many native tribes thought of the bear as a "god". American Indians saw that these grizzlies were large and very strong animals that could move quickly in spite of their size.
Hope this helps.