Atontado translates to "dazed" or "smitten." It's a vivid word that describes being so overwhelmed by something or someone that you're left a bit foolish or stunned.
In the song, the singer uses it to express how completely captivated and almost foolishly in love he is with the woman. He sings, "Algo tiene que me trae todo atontado" (She has something that leaves me completely dazed), perfectly capturing the feeling of being head-over-heels and a little out of his mind because of her.
This song is about a man who keeps falling harder for a woman even though the people around him think he shouldn't. Every verse admits that walking away gets harder each time, and that he can't fully explain to anyone else what draws him in so strongly.
He brushes off the advice and warnings from friends, telling them that if they felt what he feels, they would understand, and they would make the same choices he's making.
By the end, he's decided this is his own life to live. Their opinions don't need to match his feelings for the relationship to be worth it to him.