
The Ojibwa (Chippewa)   believe that night is full of both good and bad dreams. When a dream  catcher is hung above the place where you sleep it moves freely in the  night air and catches the dreams as they drift by. The good dreams,  knowing their way, pass through the opening in the center of the webbing  while the bad dreams, not knowing the way, are caught in the webbing  and destroyed at the first light of the morning sun. 
There are many variants to the dream catcher legend, some which say both  the good and bad dreams are captured and some which say the good dreams  slide down the feather to those sleeping below. Although the Ojibwa are  credited as the first people to use Dream Catchers many other Tribes  and Native peoples have adopted Dream Catchers into their culture. Even  though the designs and legends of Dream Catchers differ slightly,  the  underlying meaning and symbolism is universal and is carried across  cultures and language barriers.   
Everybody dreams.
Long ago when the world was young an old Lakota spiritual leader was on a  high mountain and had a vision. In this vision, Iktomi, the great  trickster and teacher of wisdom, appeared in the form of a spider.  Iktomi the spider picked up the elder's willow hoop which had feathers,  horsehair, beads and offerings on it, and began to spin a web. He spoke  to the elder about the cycles of life; how we begin our lives as  infants, move on through childhood and onto adulthood. Finally, we go to  the old age where we must be taken care of as infants, completing the  cycle. "But," Iktomi said as he continued to spin his web, "in each time  of life there are many forces; some good and some bad. If you listen to  the good forces, they will steer you in the right direction. But, if  you listen to the bad forces, they'll steer you in the wrong direction,  and may hurt you. So these forces can help or can interfere with the  harmony of Nature."

While the spider spoke, he continued to weave his web. When  Iktomi finished speaking, he gave the elder the web and said, "the web  is a perfect circle with a hole in the center. Use the web to help your  people reach their goals, make good use of their ideas, dreams and  visions. If you believe in the Great Spirit, the web will catch your  good ideas and the bad ones will go through the hole." 
The elder passed on his vision to the people, and now many Indian people hang a dream catcher above their bed to sift their dreams and visions. The good is captured in the web of life and carried with the people, but the evil in their dreams drops through the hole in the center of the web and are no longer a part of their lives.
The elder passed on his vision to the people, and now many Indian people hang a dream catcher above their bed to sift their dreams and visions. The good is captured in the web of life and carried with the people, but the evil in their dreams drops through the hole in the center of the web and are no longer a part of their lives.
Story source here & here
Images sources unknown but greatly appreciated