Encule is a popular Colombian slang term for a powerful, all-consuming infatuation. There's no perfect one-word translation in English, but think of it as being completely 'hooked' or smitten with someone.
It's a very strong word, and in the song, KAROL G uses it to express a total surrender to her feelings. She sings 'El encule me ha ganado' (The infatuation has won me over), admitting that she went from wanting a casual fling to being unable to think about anyone else.
Have you ever started something casual with someone, only to find yourself catching feelings? That's exactly what KAROL G is going through in "CAIRO". She kicks things off by admitting that maybe it's the alcohol talking, but she has to confess what she's been feeling for a while. They both knew the deal: "Sé que el amor no estaba en el contrato" (I know love wasn't in the contract). She swore she wouldn't get attached, but now she's breaking all her own rules.
Her friends are warning her that this guy is a player, or as she puts it, "medio perrito" (a bit of a dog), but she's not worried. She thinks she can change him! She went from a strict one-night-only policy to her new "plan favorito" (favorite plan) being just staying in his bed. She keeps telling herself, "No estoy enamora' pero falta poquito" (I'm not in love, but I'm close), but her actions say otherwise. She's calling him 'Amor', taking care of him when he's sick, and can't even sleep unless he's there. She's pushed everyone else away for him, and now she's leaving the choice up to him: "Te quedas o te vas, ya tú verás" (You stay or you go, you'll see).