When someone says “eye tattoo,” there are different things that they may be referring too. In this case, I am only referring to a procedure that is known as corneal tattooing. Corneal tattooing is most often done for problems of the iris, which is the colored part of the eye.
Why? One of the functions of the iris is to regulate the light coming into the eye where it can be sensed by the retina. If there are holes in the iris, it can allow light in that can potentially cause confusing image formation. Problems of the iris can also just allow too much light into the eye.
If direct iris repair is not the preferred option (or not possible), there is the option of “tattooing” the cornea. The cornea overlies the iris, so if an ophthalmologist darkens the part of the cornea that is over a problematic area of the iris, that functionally has the effect of blocking the light, similar to what the iris “should” have been doing.