Why is part of the sky red/orange/pink during sunset/sunrise, yet it isn't those colours during the day?
First, we need to understand what is colour. The light that we see behaves like waves. Very similar to waves you see in the ocean. Of course, there are some basic differences, but the principle is very similar. One difference is the wave-length - the length between two peaks. While for water waves it is typically on scale of centimeters to meters, in light it is very small - and for the light we see it is typically around 0.5 micro-meter (micro = 1/(1 million)) which is ~500 nano-meter. The difference between the colours is the wavelength: red colours have longer wavelength - around 700 nano-meter than blue colours, whose wavelength is ~450 nano-meters.
Sun light is composed of multicolour spectrum - just like the rainbow. In the middle of the day, the sun appears yellow - white: white is what you get when you combine all the different colours together.
On its way to our eyes, the beam of light from the sun has to pass through the earth's atmosphere. The atmosphere is not empty: it is made of gases, mainly nitrogen (78%) and oxygen (21%), water vapour and other chemical molecules. As the light ray passes through the atmosphere, it is scattered by the molecules. This scattering, known as Rayleigh scattering after Lord Rayleigh, depends on the wavelength of the light: the blue (shorter) wavelength are scattered much more efficiently, that is into much greater angles, than red (long) wavelengths. The scattering at 400 nano-meter is nearly 10 times more effective than the scattering at 700 nano-meters.
In the middle of a day, when the sun is high in the sky, light reaches us most directly, as it passes through less atmosphere on its way. Therefore, there is less scattering: the sun appears brightest, and only the blue light is scattered effectively. Thus, when we look at parts of the sky that are away from the sun, the sky looks blue - we are simply seeing the scattered sun light.
However, during sunset and sunrise, the sun is low in the sky. Therefore, light from the sun has to pass through longer portion of the atmosphere. When this happens the blue part (and most of the green part) of the spectrum is scattered away from us, leaving only the longer wavelength - red and orange for us to see. This effect is further enhanced if the atmosphere is polluted - either by human activities, or by natural causes, such as volcanoes.
Interesting webpage on the subject: