Indispensable means "essential" or "indispensable." It's a strong word that emphasizes the absolute necessity of something.
In the song, the narrator advises the new partner to be "indispensable" to the woman, implying that they should make themselves so vital to her happiness that she wouldn't consider leaving them, just as she left the narrator. It's a poignant and somewhat ironic use of the word, highlighting the narrator's past mistake and warning the new lover.
In "Disculpe Usted" [Excuse Me], Jary Franco plays the part of a former lover giving some unsolicited, but well-intentioned, advice to his ex-girlfriend's new partner. He starts by saying, "Disculpe usted, no quiero molestarlo" [Excuse me, I don't want to bother you], but then immediately launches into a list of warnings and tips. It's a pretty bold move, right?
He tells the new guy, "No quiero que le pase lo que paso conmigo" [I don't want what happened to me to happen to you], implying he messed up and lost her. He then spills all her secrets: she loves serenades, waking up to a kiss, and especially a beautiful red rose because "Ese detalle es el que más la vuelve loca" [That detail is what drives her most crazy]. But the biggest warning is about trust: "Mas nunca dude de su amor no es de esperarse, ella es mas fiel de lo que pueda imaginarse" [Never doubt her love, it's not to be expected, she is more faithful than you can imagine]. He ends with a blunt truth: "Que nunca cruce por su mente traicionarla, eso mi amigo, eso la mata" [Never let it cross your mind to betray her, that my friend, that kills her]. It's like he's saying, "I learned the hard way, so you don't have to!"