Aferrarse means “to cling to” or “to hold on stubbornly,” often to a person, idea, or hope. In the song, “No te aferres a un imposible” means “Don’t cling to the impossible,” vividly describing someone who cannot let go of a love that is no longer possible.
This is a breakup song where the singer is the one leaving, and he spends the whole thing apologising. It opens with "Perdona si te hago llorar" [Forgive me if I make you cry] and "Perdona si te digo adiós" [Forgive me if I say goodbye], and his excuse is the oldest one there is: "Pero es que no está en mis manos" [But it's just not in my hands]. He has fallen for someone else, "Me he enamorado" [I've fallen in love], and he says it twice, in two tenses, as if to make sure it sticks.
Then it gets awkward in a very honest way. He tells his ex "Soy honesto con ella y contigo" [I'm honest with her and with you], then hits her with "a ti te he olvidado" [you, I've forgotten] and, right after, offers "seremos amigos" [we'll be friends]. Bold. He also reminds her that she walked out first: "tú te fuiste sin decirme nada" [you left without telling me anything]. A useful bit of slang for learners is "Ya no te hagas" [stop pretending], from hacerse, which in casual Spanish means acting like you don't know something. The ending is sweet: the new love is "un ser divino" [a divine being] who taught him "A olvidar / Y a perdonar" [to forget / and to forgive]. Turromantikos set all of this to a cumbia beat, so the heartbreak is very danceable, and they sign it off with "Con sabor" [with flavour].