Gabán translates to "overcoat" or "cloak". It's a charmingly old-fashioned word that isn't commonly heard in everyday Spanish, making it stand out.
In the song, the phrase "Que no se le enrede el gabán, paisano!" is a playful, colloquial warning meaning "Don't let your overcoat get tangled, countryman!" It's a colorful way to tell someone to be careful or not get into trouble, adding a touch of rustic charm to the lyrics.
Joan Sebastian spends this whole song refusing to believe the breakup is real. Nearly every chorus repeats the same lines: "Que no, que no" ("No, no") and "Que no te asombre" ("Don't be surprised"), a man talking himself out of the bad news his partner keeps trying to deliver.
He knows exactly what's coming. "Yo sé que te puedes marchar" ("I know that you can leave") and "Sé que me podrías matar" ("I know you could kill me") admit the worst outright, then he swaggers right past it: "Traigo 5 ases" ("I bring 5 aces"), as if confidence alone could keep her from walking out the door. The shouted "¡Ándele!" ("Go ahead!") and the long "Ay, ay, ay ay ay ay" ("Oh, oh, oh, oh, oh, oh") are the mariachi joining in, which is part of the joke: everyone in the room can hear he's about to lose.