Dark circles are a blue, red or violet blemish on the lower eyelids. The dark pigmentation is often associated with minor sleep deprivation. In this case, the coloured under-eye is caused by the blood vessels dilatation.
The problem can also be genetic; some individuals can have a good night sleep and still have pigmented under eyes.
Ageing is another origin of dark under-eyes. The skin under the eye become thinner, making the blood vessels visible and causing the dark tint under the eyes.
Here are the solutions available at Epilium & Skin: