hubieras ido is a form of the verb ir (to go) in the past perfect subjunctive. This special mood is used to talk about hypothetical 'what if' situations in the past that didn't happen.
In this iconic song, the title itself, "Si no te hubieras ido..." (If you hadn't gone...), sets a tone of deep regret. The singer uses this phrase to imagine how happy his life would be, creating a powerful and heartbreaking contrast with his current reality of loss.
This song is a straight-up, gut-punch of a breakup song. The singer from Maná lays it all out: someone has left, and now his whole world feels wrong. He wakes up thinking of them, saying, "Te extraño más que nunca y no sé qué hacer" (I miss you more than ever and I don't know what to do). Life has become something to just get through, and he feels so changed by the loss that even his own reflection looks wrong: "El espejo no miente / Me veo tan diferente" (The mirror doesn't lie / I look so different).
He feels completely out of step with the world around him. While everyone else goes about their day, "La gente pasa y pasa siempre tan igual" (People pass by, always the same), he thinks "El ritmo de la vida me parece mal" (The rhythm of life seems wrong to me). The song keeps coming back to one simple, powerful idea, repeated over and over: "Si no te hubieras ido sería tan feliz" (If you hadn't left, I would be so happy). It's a raw look at how one person's absence can make everything else feel empty.