Sottane literally translates to "skirts" or "petticoats". While it might seem like a simple word, its use in this song is quite evocative and less common than a generic word for clothing.
In "Cammina Bambina," Gianluca Grignani sings about a "gioco di sottane" (game of skirts), which implies a flirtatious or seductive game. It's a more poetic and slightly old-fashioned way to refer to a woman's allure, making it an interesting and memorable word choice that hints at the song's romantic and somewhat playful tension.
Gianluca Grignani's "Cammina Bambina" is a man talking himself out of an attraction he knows is bad for him. He opens by asking "Quanto tempo mi ci vuole per capirti un po'" (how much time do I need to understand you a bit), and admits that "Basta poco per innamorarsi di te" (it takes little to fall in love with you). She plays with him, her "gioco di sottane" (game of skirts), and he confesses "Io sono un uomo non rimango certo indifferente" (I'm a man, I certainly don't stay indifferent). So he tells her to "scendi dal tuo trono di sesso" (get down from your throne of sex).
The second verse turns the tables. He says he needs love, "ho bisogno d'amore", and asks "Che donna sei se tu rimani sempre indifferente" (what kind of woman are you if you always stay indifferent). The chorus is his answer: "Cammina, cammina bambina" (walk, walk, girl), because "Se la mia strada è fatta di donne / Tu non sei quella per me" (if my road is made of women, you're not the one for me). The repeated "cammina" works as both a brush-off and a phrase he seems to repeat to convince himself.