Eczema is a general term encompassing various inflamed skin conditions. One of the most common forms of eczema is atopic dermatitis (or "atopic eczema"). It is most often characterized by dry, red, extremely itchy patches on the skin.
In people with eczema, the inflammatory response to irritating substances (such as tattoo ink) overacts, causing itching and scratching. This can make healing the tattoo uncomfortable and could produce scarring.