There are many tribes of Native American Indians, and thus it is only possible to generalize the most common meaning of the Turtle symbol.
The turtle holds a very important place with regards to the religious beliefs of the Native Indians. The symbol of the turtle is perhaps one of the most popular amongst them all and it is to be found in almost all Native American Tribes. It is also one of the oldest Native American animal symbols.
The meaning of the Turtle symbol signifies good health and long life (the turtle has great longevity living up to 150 years).
According to Native American legends and myths of the Eastern Woodland tribes the turtle played a part in their Creation myth. The Earth Diver turtle swam to the bottom of the water that stretched across the world. He surfaced with the mud which the creator used to make the earth. The hard shell of the turtle represents perseverance and protection.
The symbol of the turtle in Southwest tribes such as the Hopi and Navajo represents water, which of course is a much sought after commodity in desert regions.
The turtle symbol also represents the Earth Mother. The earth mother features in many Native American myths and legends and is honored for saving mankind from the Great Flood. The turtle symbol of the earth mother represents her stoic ability to carries the heavy burden of man on her shell.
Information source: Wikipedia