Atado literally means "tied". It is the past participle of the verb atar (to tie).
In this song, Alvaro Soler uses it metaphorically in the powerful line "Atado a tu cuerda" (Tied to your rope). This paints a vivid picture of feeling emotionally trapped and dependent in a relationship, unable to leave. He's begging his partner to "suelta de una vez" (let go at once), making atado a key word that expresses the song's central feeling of desperation.
Ever been in a relationship where you just can't figure out what the other person is thinking? That's exactly what's happening in this song. Alvaro Soler is completely fed up with the mixed signals he's getting. He sings, "Ando buscando en tus besos tu voz / Dicen que sí, luego dicen que no" (I'm looking for your voice in your kisses / They say yes, then they say no). He feels like he's being toyed with and directly asks, "¿cuánto más / Tienes que jugar conmigo?" (how much more / do you have to play with me?). He's reached his limit and just wants a clear answer, one way or another.
He's so desperate for clarity that he's practically begging for the end, even if it hurts. He feels like he's "Atado a tu cuerda" (Tied to your rope) and tells his partner to "Suelta de una vez" (Let go at once). He remembers all the "promesas eternas" (eternal promises) that are now just forgotten, packed away "en un cajón" (in a drawer). He's tired of waiting and says he "no aguanto más" (can't take it anymore). It's a straightforward plea to stop the games and face the truth.