The sun gives off a huge amount of ultra-violet radiation which, as well as damaging our skin, damages the pigments in things which are dyed. The result in a loss of the reflective properties of the pigments, so the colours become less vivid.
Sunlight contains a wide spectrum of light. Each object absorbs or reflects the different colours of light falling on it. When a substance such as fabric dye is exposed to sunlight, the energy in the sunlight causes a reaction within the fabric which causes the dye to lose its colour. Blue fabrics tend to fade most rapidly in the sun, because they react more with the particular colours in the sunlight.
To add to what the others have said- the colour of a substance depends on the energy levels of the atoms inside it. So when ultra violet radiation meets the atoms in the dye it must transform the energy levels so that it doesn’t give out the same colour in some way- hopefully this makes sense!
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