Satellites don't shine with their own light; if they did we would probably see more satellites than stars in the sky!
We only see satellites when they reflect sunlight back to Earth. But at night—when satellites are in the shadow of Earth—there is no sunlight to reflect. And in the day, when the sun dominates the sky, satellites are hidden against the bright blue of the atmosphere.
So how can we ever see satellites at all?
They're relatively high up—anywhere from 150 to 36,000 kilometers (90 to 22,000 miles)—so even when the sun is beneath the horizon for Earth-bound observers, they can still be in the path of the sun's light.
Which means the best time to see most satellites is during twilight—an hour or two before sunrise or after sunset.