The first sentence of the chapter that contains the reference to Turtle Lake is "The reservation is beautiful." In this chapter, Junior enjoys the beauty and familiarity of the reservation, which will always be home to him. I believe that Turtle Lake, which is the focus of a number of Indian legends and myths, can be considered to be a symbol of the rich Indian culture that characterizes the Spokane nation that must call the reservation their home.
In addition to representing Indian culture, Turtle Lake has a distinctiveness that is unique and mysterious. Scientists have concluded that the lake is "an ancient and dormant volcano crater," with incredible depth, like roots going "all the way down to the center of the earth." In like manner, the Spokane tribe has a history that is goes back for generations and is deeply rooted, in history, and in the earth.
The horrifically frightening tale of Stupid Horse, who drowned in Turtle Lake, is typical of the ghost stories Indians love. The story was scary enough that for years, no one would swim in Turtle Lake, but as time passed, the people forgot their fear and began to swim in the lake again. Junior's observation that "people forget" is significant. The Indians are now trapped on the reservation, and although they are victims of racism and oppression, part of the blame for their situation lies in their own passivity and inertia. In Junior's estimation, the Indians have forgotten their rich and noble heritage, as symbolized by Turtle Lake, and, crushed by the treatment they have received at the hands of white society, have simply given up (Chapter 29 - "Talking About Turtles").
The story of the Turtle Lake is significant because it symbolizes something. It symbolizes determination of the Stupid Horse, even though it is dead. The horse kept itself from rotting and kept coming back to the Turtle Lake. This story also relates to Arnold's life, as he was determined to go teducation and have a good education. The above answer is also right, but I looked at it from a symbolic way.