Sunlight consists of light of different wavelengths, which we perceive as different colors – from short-wavelength blue to long-wavelength red. When this light hits air molecules (mainly nitrogen and oxygen), it gets scattered in all directions.
This effect, called Rayleigh scattering, affects short-wavelength blue light much more strongly than long-wavelength red light – blue light gets deflected in all directions far more often. Looking anywhere in the sky during the day, without looking directly at the sun, you mainly see this scattered blue light.
At sunset, the light travels a much longer path through the atmosphere. The blue light gets scattered so many times that it disappears from the direct line of sight, while reddish light tends to survive the journey – which is why the sky then appears orange to red.