There are hundreds of Native American tribes who have evolved and developed their beliefs and rituals over the span of hundreds of years. This being the case, it is difficult to pin point one single, specific meaning of feathers to Native Americans.
However, I have read legends in which the Hopi used turkey feathers in various symbolic placements and rituals. The number of turkey feathers used is four. The turkey is a symbol of the wildness of the Earth, and the number four represents the four winds. Together, this is a symbolic message that the Earth is a wildnerness that man can never control.
I also know that the Sious used feathers in headdresses (reserved for the higher-minded or wiser souls, tribe noblemen, soothsayers, etc). Twenty eight feathers were used in Sioux crowning rituals. Twenty eight is sacred to the Sioux to represent the life of the Moon breathes within a span of twenty eight days. There are also twenty eight ribs within the cage of the buffalo, which was/is sacred to this tribe.
Also among the Sioux, the Eagle (specifically, the Golden Eagle) was a sacred symbol, and twelve of her feathers were used in ritual, ceremonial events to signify the number of months in the year as well as the twelve symbolic rays of the sun.
Other information on feathers: