Edén refers to the Garden of Eden, a biblical paradise. It's a beautiful, poetic word used to describe a perfect, idyllic place or state of being.
In this classic salsa song, Eddie Santiago sings, "Yo no te prometí, nunca te prometí el edén" (I never promised you, I never promised you Eden). He uses this powerful image to be honest with his lover, admitting he isn't perfect and can't promise a flawless relationship. This makes his confession that he needs her ("tú me haces falta") feel even more sincere and profound.
Eddie Santiago starts this song with some incredible honesty! He tells his ex-lover, "Yo no te prometí nunca te prometí serte fiel" (I never promised you, I never promised to be faithful to you). He's not trying to pretend he was perfect. Instead, he argues that while he couldn't promise forever, his feelings were real: "cuando dije amar te amé" (when I said I loved you, I loved you). He explains he was too afraid of failing her to make big promises.
But now, everything has changed. He left, and he was miserable. The chorus is his big confession: "Tú me haces falta" (I miss you). Without her, he says, "las noches son un fantasma son un castigo" (the nights are a ghost, they are a punishment). He has realized that if he's going to love anyone, "si tengo amores que sean contigo" (if I have loves, let them be with you). He is coming back because of their shared memories, and this time, he's ready to commit in a way he wasn't before, promising his return is for "tiempo indefinido" (an indefinite time).