Tattoos (like most art), are deeply personal and their true meaning isn't necessarily meant to be understood by a casual passer by. "If eyes are the windows to the soul, tattoos visualise the song the soul sings". Capturing that song takes more than just squeezing the trigger and hoping for the best.
A tattoo will add another dimension to a portrait. Capturing the right balance of "just a photo of a tattoo" and "a portrait of a person where the tattoo augments the subject in telling a story" is all important. Light, shadow, textures, detail, soul.
It can be a balance between revealing the individual in an appealing pose, ensuring the right detail of the tattoo(s) is captured and that the location (or context) surrounding the subject doesn't draw focus from the subject's story. In other words, making the portrait about the person, not just the ink they're wrapped in.