Tatuado means "tattooed". While it can refer to a literal tattoo, Ivan Cornejo uses it here in a deeply metaphorical and poetic way.
He sings, "Y tatuado en tu piel / Lo que nunca se dio" (And tattooed on your skin / Is what never came to be). This powerful image suggests a past regret or a failed relationship is permanently and painfully etched onto someone, like invisible ink. It's a beautiful way to describe a memory that you simply can't escape.
This song is about watching someone you used to love try to party away their sadness. Ivan Cornejo sings from the perspective of an ex who sees a woman he once knew completely change. She goes out pretending to be happy, but he sees right through it. He describes her getting ready with a powerful image: “Pinta sus labios color rosado / Vestido negro, y por dentro su llanto” (She paints her lips pink / Black dress, and inside her tears). It’s a perfect summary of someone putting on a brave face for the world.
He feels like he doesn't even recognize her anymore, asking “Y la mujer que tanto amé / ¿A dónde se me fue?” (And the woman I loved so much / Where did she go?). He knows she's just trying to feel something for a moment, but believes her fun is temporary, saying “se lo lleva el viento” (the wind carries it away). He seems confident that eventually, she'll find her way back to him, because he's the only one who sees her true self.