Small grammatical point upstream: we do not say a ring, but a ring. But a ring, what is it first? A dark circle is a variation in the color of the skin located below the eye. In fact, the region of the eye is very vascularized, that is to say that it contains a lot of blood vessels, but also lymphatic vessels, which are used for skin circulation. These blood vessels can be arteries, which carry blood from the heart to the organs, but also veins, which bring the blood used by the organs back to the heart.
Lymphatic vessels circulate lymph: a biological fluid that has a composition similar to blood plasma, which carries white blood cells and evacuates waste products from cells. You have understood that the appearance of dark circles is partly linked to the circulation of blood and lymph, but why do they appear more in this place than in another area of the body?
To understand this, watch the explanatory video at the top of the article.