That saying reflects a very old Lakota philosophy. They believe that the heavens are a mirror for the earth. What happens up there will happen down here in some way, shape or form. Many of the Lakota ceremonies took place when the sun was in a specific constellation. For example, when the sun enters the constellation Dried Willow (Triangulum and part of Aries) the sacred spring ceremonial round begins.
Now, I know just what you're thinking. "Wait a minute. You can't see stars in the day time. So how can the sun be in a constellation?" The answer is that you look for the 'opposite' constellation, the one that's on the other side of the earth from Dried Willow. You can see that, because the night side of the Earth faces it when the day side faces Dried Willow, as illustrated in the grapic on the right. The sun is 'in' Dried Willow when Antares rises early in the evening, just south of the ecliptic (the line that the sun traces out as it crosses the sky).
The sun played a major part in many other Native American cultures. The Pueblo believed that the sun was directly responsible for all life in some way or another. They watched the rising and setting of the sun carefully. Because the Earth is slightly tilted, the sun rises and sets at different places on the horizon. At the equinoxes in the spring and fall it rises due east and sets due west, but at the summer and winter solstices it rises in the northeast and southeast respectively and sets in the northwest and southwest
The graphic to the left illustrates the solstices and equinoxes. The lines that go
from east to west are the paths of the sun at the solstices and equinoxes. The line
that runs from the north to the south cutting the sky in half is called the
The solstices were times of much ceremony for the Pueblo. At the summer solstice, they encouraged the sun to stay in the northern sky for as long as possible to provide warmth and light for the crops. At the winter solstice, they would entreat the sun to 'turn around' and move to the north again.
Not all tribes used the sun, however. The Navajo used the stars as their guides. They watched for certain constellations to rise and from this they determined the time for planting and the seasons. The constellation known as Revolving Male (Ursa Major and the pole star) would be parallel to the horizon when they started to plant, and when Dilyehe (The Pleiades) was in the northeast early in the morning, it is time to stop planting. The first frost would come soon after Dilyehe could be seen in the northeast in the evening.
The Navajo used the stars as more than just a calendar. They looked to them for healing and problem solving through a method known as stargazing. They would look at the brightest stars through any kind of glass like material and use the colors they saw to determing the proper ceremony to perform in order to resolve their problem. It's like holding a prism up and letting the sun shine through it; you see a rainbow. The Navajo method is the same idea; they looked at the rainbow that the star made when you looked at it through a glassy material.
Stars aren't the only thing you can see in the night sky. If it's the right time of year and you know where to look, you can see the Perseid Meteor Shower. Every now and then, you might be able to see a meteor (shooting star) or a even a comet. Different Native American tribes had different explanations for what things like these were. Some thought that meteors were omens of sickness and death, others believed that they were spirits on their way to the afterlife. One belief that I found particularly interesting was the Kiliwa belief that meteors were the urine of the constellations Xsmii. "Tinkle, tinkle, little star... " (sorry, I just couldn't resist.)
There is also an Ojibwa story about Ghenondahwayanung (geez, say that three times fast), "Long Tailed Heavenly Climbin Star". Ghenondahwayanung is expected to one day return and destroy the earth. In the Ojibwa creation story, Ghenondahwayanung comes down to the Earth and scorches everything except the Ojibwa tribe. They were warned by a spirit, and they rolled themselves in the mud in a bog to protect themselves from the heat.