Tattoos are typically the most common variety of body modification for both players and characters. Did your character choose their own tattoos or were they chosen for your character?
If they chose their own, did they choose a random one off the wall? Or did they have a tattoo custom designed just for them which might even have a special meaning just for your character?
If the tattoo was chose for your character, was it of religious or criminal importance? Or was it perhaps designed to be a secret map or message that even your character may not understand?
Physical body modifications, while more common in sci-fi related RPGs, such as Warhammer 40,000, can be made for numerous reasons.
Was your character gravely injured and needed to replace a limb (e.g., legs, arms, hands, etc.) or other body part with a suitable replacement?
Did your character choose (or were they forced) to undergo some top-secret cybernetic enhancement to make them bigger, stronger, or faster?
Was it medically necessary for them to replace a failing body organ (e.g., heart, lung, eye, etc.) in order to stay alive?
Body modifications and tattoos can potentially have a lot of implications within your game's world and mythology. These implications can include things like "tattoos containing secret prophecies" or "cybernetic arms containing hidden rocket launchers."
Work with your DM/GM to see how your character's body modifications and tattoos might possibly influence events and interactions within your game . . . for good or evil.