Conquistar means "to conquer" or "to win over." While it can refer to military conquest, in a romantic context, it means to win someone's heart or affection.
In this song, the singer is determined to "conquistar" his partner again, implying he wants to rekindle the romance and make her fall in love with him all over again. It's a strong, active verb that sets the tone for his romantic intentions.
A man who has clearly been getting the basics wrong is trying to fix all of it in one night. He opens by owning up: "Ay, disculpa si no te he mandado flores" [Oh, forgive me if I haven't sent you flowers], then "Si me olvidé de las fechas, no es porque ya no te quiera" [If I forgot the dates, it's not because I don't love you anymore]. Thin excuse, and he seems to know it. His whole defence is the line he closes the verse on, "Si bien sabes que yo te amo a mi manera" [You know very well that I love you in my own way], which is the sort of thing you say once you have run out of better arguments.
So he plans an evening instead. She puts on her best dress and paints those lips red, he switches the phone off, and it all comes down to "Un vino a la luz de las velas, tú y yo nomás" [A glass of wine by candlelight, just you and me]. Grupo Frontera let the accordion do most of the pleading, and the chorus promise, "Voy a volverte a conquistar" [I'm going to win you over all over again], lands somewhere between romantic and slightly desperate. The best line is "Hoy se va a hacer lo que me pida la reina" [Today we do whatever the queen asks of me]. For one night, she picks.