Juré is the past tense of the verb jurar, meaning 'to swear' or 'to promise.' It's a dramatic word used to express a deep, heartfelt commitment.
In "El Perdón," the singer uses it to confess, 'Yo te juré... este eterno amor' (I swore... this eternal love to you), revealing the core of his regret and setting the stage for his desperate plea for forgiveness.