Amarrado literally means "tied up" or "bound." While it can refer to physically tying something, it's often used metaphorically in Spanish to describe being emotionally trapped or strongly attached to someone or something.
In "Calmarme," Amenazzy sings, "Eres droga, eres pecado / Por eso me tienes amarrado" (You are a drug, you are a sin / That's why you have me tied up). Here, amarrado vividly conveys the feeling of being completely captivated and unable to escape the intoxicating allure of the person he's singing about, highlighting a powerful, almost addictive, connection.
Amenazzy spends this whole song trying to talk himself down. He opens by asking for a minute alone with her, "Déjame hablarte" [Let me talk to you], and by the chorus he has already lost the argument with himself: "Tengo que calmarme, calmarme" [I have to calm down, calm down], "Porque si no voy a terminar perdiendo" [Because if not, I'm going to end up losing]. It plays less like a love song and more like a guy narrating his own bad decision as it happens, caught between how good the attraction feels and how obviously it ends badly.
By the second verse the reason for his panic is out in the open. She is not choosing him back. "Y tú solo una aventura" [And you, just an adventure] is the whole plot in one line, and he says it plainly a few bars later: "Vas ganando y yo perdiendo" [You're winning, and I'm losing]. There is no twist or resolution here, just a guy who knows exactly what he is walking into and goes anyway, which is what makes that chorus hit again every time it loops back around.