Desacató comes from the verb desacatar, which means to disrespect or disobey. However, in urban Latin music, especially in the Dominican Republic where this artist is from, it's often used colloquially to mean 'got out of control' or 'went wild' in a celebratory or uninhibited way.
In the song, it's used to describe a girl who 'se dejó del novio' (broke up with her boyfriend) and then 'se desacató' (let loose/went wild) with the singer. It implies she's shedding her inhibitions and enjoying her newfound freedom.
The whole track hangs on one word repeated until it stops being a word and turns into percussion: "Toque, toque, toque" [touch, touch, touch]. Ezzy R opens by explaining how much work she was, “Me tomó como tres horas en sacarte una sonrisa” [it took me about three hours to get a smile out of you], and then lands the line the title comes from, “Que del novio se dejó conmigo se desacató” [that she left her boyfriend and went wild with me]. He is not telling you about a romance. He is reporting a result.
Leo RD takes the second half and turns the boasting up. She has money but comes from Los Mina, a barrio in Santo Domingo; the police stopped him at the party; “El peine en mis pistolas y lleno de balas los míos” [the clip in my guns and my guys loaded with bullets]. He signs off with the line the song keeps circling back to, “Como en diez, quince, veinte años nace otro como yo” [in about ten, fifteen, twenty years another one like me is born]. Everything between the verses is that hook word again, eight to a bar, and at 2:11 the song ends before the repetition can wear out.