Do you know what a spectrum is? These are all the colours you see in a rainbow or a prism. These colours make up the varying wavelengths of white light, only we don't see them as such unless they are broken or split up through a process called 'refraction.'
The colour something "is" is actually the colour not absorbed by an object but reflected back instead. Which colour is absorbed or reflected back depends on its particular wavelength and that wavelength's capacity to be absorbed or reflected by a particular object.
For example, when all colours are absorbed, what you see is 'black' - nothing comes back. Along with light, some heat is also absorbed. That is why a black asphalt pavement is so steaming hot on a summer day! (You can take a thermometer and verify the difference in temperature colours make by placing it on a white piece of paper, then a black one.)
So the sky is 'blue' because the wavelength of white light most easily reflected back to Earth from the atmosphere is the one corresponding to blue. As sunset approaches, these colours change as the angle of sunlight shifts, favouring the wavelength in white light corresponding more to reddish tones.(A part of this is also due to dust in the air, but this is another factor and subject!)
Does this answer your question? In short, the 'colour' you see is actually the wavelength of white light rejected by a particular surface, kind of like a ball bouncing back from off an invisible wall instead of passing right through.
Check out the references below for more information, and another experiment you can do.