Batuta literally translates to "baton", as in a conductor's stick. It's an interesting word because it's not commonly found in everyday Spanish songs.
In this song, Darío Gómez uses "batuta" in a playful riddle, asking the listener to guess what object he's describing. The word is used to describe something that guides or directs, much like a conductor's baton, but in a more suggestive and humorous context within the song's double entendres.
Darío Gómez is playing a fun game with us in "El Enigma"! He's got a secret, and he's challenging us to guess what it is. He starts by saying, "que no me adivinan el secreto que tengo aquí" [you won't guess the secret I have here], promising to leave us thinking.
He gives us a bunch of clues, describing something that "las mujeres les roban la cabeza" [steals women's heads] and "tiene cabeza que no sopla pero infa" [has a head that doesn't blow but inflates]. He also mentions it "no es ningún perezoso y siempre vive colgado en el borracho" [isn't lazy at all and always hangs on the drunkard]. It's a bit cheeky, and he even asks, "Darío no me crea bruto no creas que nadie sabe" [Darío, don't think I'm stupid, don't think nobody knows]. He's having a laugh, and by the end, he's still teasing us, asking, "dígamelo darito que la misma quede yo que no hay por debajito fue lo que mi Dios le dio" [tell me, Darito, what I have that's the same, what God gave me from below]. It's a classic Darío Gómez move, full of double entendres and Colombian humor!