Garantizo comes from the verb garantizar and means "I guarantee". This word is especially interesting because it sounds quite formal, almost like something you'd hear in a business contract, not a romantic song.
When Prince Royce sings "te garantizo mi amor", he's elevating his promise. He's not just saying he loves her; he's declaring his love is a sure thing, an unbreakable commitment you can count on, especially when others are trying to cast doubt on their relationship.
This song is a super romantic declaration of love against the world! Prince Royce is telling his partner that they are meant to be, singing, "Tú eres para mi yo soy para ti" (You are for me, I am for you). He's all in, promising, "Te entrego mi vida y mi amor hasta el fin" (I give you my life and my love until the end).
The main problem is that her friends are talking trash about him. They say he's a bad guy and even suggest he's cheating: "They tell you that I might be going around cheating". But he insists they're just jealous haters and that their relationship is only their business. He reminds her of how they met in school and how their love has grown since then, making a promise that nothing would destroy it. He gets really dramatic, saying he's willing to die for her, which is a lot, but it shows how serious he is about keeping their love alive.