Clavada comes from the verb clavar, meaning to nail, stick, or embed. While it can refer to something literally nailed, in this song, it's used metaphorically.
Bronco sings, "Como espina que queda clavada" (Like a thorn that remains stuck). This vivid imagery describes a deep, persistent pain or feeling that is impossible to remove, much like a thorn embedded in the skin. It's a powerful way to express enduring emotional hurt.
Bronco's “Corazón Duro” turns heartbreak into a dare. The narrator can't do what the other person is asking — “Que me olvide de ti, me lo pides” [You ask me to forget you] — because there's nowhere in him this person hasn't reached: “Si en cada pedacito de mí tú vives” [If you live in every little piece of me]. So instead of forgetting, he hardens. The title phrase becomes armor: “Como piedra que no siente nada” [Like a stone that feels nothing], “Como espina que queda clavada” [Like a thorn that stays stuck] — pain turned into a shield rather than something to heal. By the end he isn't pretending it doesn't hurt; he's just decided to survive it anyway: “Sobrevivo aunque tú no me quieras, corazón” [I survive even if you don't love me, heart].