Delatarnos comes from the verb delatar, meaning to betray, denounce, or give away. The reflexive ending -nos means "us", so delatarnos means "to give ourselves away" or "to betray us".
In the song, Ricardo Montaner sings, "Es tan fácil delatarnos que morimos por amor" (It's so easy for us to give ourselves away that we're dying for love). This word beautifully captures the idea that their hidden love is so strong, their actions and glances easily reveal their true feelings, even when they try to hide them.
Ricardo Montaner isn't ready to let go. In "Aunque Ahora Estés Con Él" ("Even If You're With Him Now"), he tells a woman it's unfair to ask him to forget her: "Injustamente estás pidiendo que te olvide" [You're unfairly asking me to forget you]. He's convinced she still loves him too: "Es tan fácil delatarnos que morimos por amor" [It's so easy to give ourselves away, that we die for love].
The chorus is his vow: "Yo te amaré, aunque no estés a mi lado" [I will love you, even though you're not by my side]. He won't stop waiting — "Yo te seguiré buscando" [I will keep looking for you], "Te seré incondicional" [I will be unconditional] — certain that she's still thinking of him: "Porque estás pensando en mí" [Because you're thinking of me], "Aunque ahora estés con él" [Even if you're with him now].