It all stems from a story about a conversation between the Great Spirit and an eagle.
Great Spirit was angry at what man (humans) were doing, and S/he (Great Spirit doesn't have a gender, so I'll use s/he when talking about him/her) planned on destroying this world again. A lone eagle went before Great Spirit and pleaded our (man's) case. Great Spirit responded that as long as at least one man lives "in balance", this world would be spared, but Eagle would have to fly around and find proof, then bring it before Him/Her. That is why the eagles fly the way they do, because S/he (Great Spirit) has them (the eagles) monitoring us, and as long as they fly, man will be safe. That is kinda the "Readers Digest" version. If you can find a copy of What My Elders Taught Me by John Boatman (my professor) I think it has one rendition of the actual story in it. It's an American Indian legend (or it could be true, metaphysically), so there might be other renditions elsewhere.