The meaning of sun tattoo is to represent life. Intuitively, we know that. There is no need for any scientific debate. It's such an obvious truth that we can feel it. The sun that gives life to all things is the center of the solar system, and everything here revolves around it. The gravity of its massive mass tethers these planets to their orbits.
In astrology, the sun also works like this. It is the center of human personality. It is the focus of various functions within each of us, our sense of identity. It gives us a sense of "being a unique person" - having our own feelings, perspectives, and ways to express our lives.
Without the sun, people will be lost, restrained by the whim of contradictory ideas and unable to move, and lose their direction in the empty universe. There's a center, there's an organization. These are the missions of the sun.