The Dream Catcher represents several meanings. All of the decorations and materials used to decorate them, all have a special meaning. A single bead in the middle may represent the spider that is on the web. Scattered beads throughout the web may represent good dreams that may have been caught throughout the night. A feather represents a symbol of breath or air which is attached so it hangs from the center of the ring. It is essential for life. A baby watching the air playing with the feather on her cradleboard was entertained while also being given a lesson on the importance of good air.
This lesson comes forward in the way that the feather of the Owl is kept for wisdom (a woman's feather); & the Eagle feather is kept for courage (a man's feather). This is not to say that the use of each is restricted by gender; but that to use the feather each is aware of the gender properties she/he is invoking. (Indian people, in general, are very specific about gender roles and identity.)
The use of gem stones, in some of the ones we make for sale, is not something that was done by the old ones. Government laws forbid the sale of feathers from our sacred birds. These include ALL Birds of Prey and include Hawk feathers, Bald Eagle feathers, Owl feather, Turkey Vulture feathers, and so on. Incorporating four gem stones into the Dream Catcher, is used to represent the four directions. Nature represents the spiritual inspiration in each.
When researching the long traditions of oral histories, storytelling has been passed down through the generations; from parent to child, grandparent to grandchild, or from one person to another. This is how the message continues to be passed on to future generations." - what a dream catcher is copied and pasted from History of the Dream Catchers, you can find more about it by going to the link that I will include as my source.
Interesting question, I too have always wondered their meaning.