Arrepentido translates to "regretful" or "repentant". It's a powerful adjective that expresses a feeling much deeper than just being sad (triste).
In the song, Carin León sings, "Estoy arrepentido, enfermo, triste y solo" (I am regretful, sick, sad, and alone). This one word reveals that he recognizes he made a mistake in the past, and this profound sense of regret is what drives him to plead for a second chance.
Have you ever missed someone so much you just had to ask if they still felt the same way? That's exactly what Carin León is doing in this song. He gets straight to the point, asking, "Quisiera saber / Si todavía me quieres" (I would like to know / If you still love me). He's not playing it cool at all. Instead, he admits he is "tan solo y triste / Cansado de extrañarte y cansado de llorar" (so lonely and sad / Tired of missing you and tired of crying).
He confesses that he tried to forget his ex but "no pude lograrlo" (I couldn't manage it). Now, he feels "arrepentido, enfermo, triste y solo" (repentant, sick, sad, and lonely). He's asking for forgiveness and a chance to "comenzar de nuevo" (start over). He believes that this person is the only one who "puedes darme la vida otra vez" (can give me life again), which is a pretty intense way to say you want to get back together!