Tattoos last so long because of insoluble ink and because of the injection of that ink into the second layer of skin. Essentially, the ink is unable to be absorbed into the body, thereby leaving it visible permanently.
Normally when skin is damaged, white blood cells appear to absorb the material into the body and away from the surface. However, the particles of tattoo ink are designed to be too large for white blood cells to remove. Consequently, the ink remains where it has been injected. The ink stays in the dermis (the second layer of skin), immediately below the epidermis (the outer layer). Tattoo removal procedures often use lasers to break up the ink particles into smaller pieces that can be absorbed into the bloodstream.
Though tattoos are designed to last forever, the ink does often fade over time. This is especially true if the ink was injected too far into the dermis or beyond it, as it will then be able to shift and spread out. Additionally, skin changes over the course of time, which affects the appearance of tattoos. Regular moisturizing with lotions can reduce fading or spreading of tattoos, as does keeping the tattoo out of direct sunlight.