The light you see when you look at the sky is sunlight that is scattered by particles of dust in the atmosphere. If there were no scattering, and all of the light travelled straight from the sun to the earth, the sky would look dark as it does at night. The sunlight is scattered by the dust particles in the same way as the light from the flashlight is scattered by particles in milk in this experiment. Looking at the sky is like looking at the flashlight beam from the side: you're looking at scattered light that is blue. When you look at the setting sun, it's like looking directly into the beam from the flashlight: you're seeing the light that isn't scattered, namely orange and red.
What causes the sun to appear deep orange or even red at sunset or sunrise? At sunset or sunrise, the sunlight we observe has traveled a longer path through the atmosphere than the sunlight we see at noon. Therefore, there is more scattering, and nearly all of the light direct from the sun is red.