Obsesionado means 'obsessed'. It's a powerful adjective that describes an all-consuming fixation on someone or something.
In this classic ballad, Enrique Iglesias uses this word to capture his intense and desperate longing for a past love. He sings, "Mientras yo vivo por ti obsesionado" (While I live for you, obsessed), perfectly summarizing the song's core emotion of being unable to think of anyone else.
This song is all about being completely stuck on an ex. Enrique Iglesias opens with a look back at a relationship, calling it "una historia de amor / Que se ha ido" (a love story that's gone). He realizes he made a mistake and now he's desperately trying to get her back, admitting, "hoy que quiero volver / Te persigo" (today I want to return / I'm chasing you). The whole song circles around this intense feeling of need and obsession, summed up in the chorus: "Necesito lo que tú me das... Y solo pienso en ti" (I need what you give me... And I only think of you).
To make things more complicated, he's actually with someone new, but it's not working at all. He says this new person sees love as just "una diversión" (a diversion), and for him, being with her is just "fingir" (pretending). All he really wants is to "huir / A tus brazos" (run away / to your arms). He's left wondering if his ex has forgotten him while he remains totally "obsesionado" (obsessed). It's a powerful song about regret and realizing you let the right person go.