Similar to the French millefeuille or mille feuille (a 'thousand sheets'), in Italy the word usually refers to puff pastry (pasta sfoglia) layered with pastry cream, and maybe a few layers of sponge cake as well.
There are also savoury versions, with spinach, cheese or other fillings. In Naples they make a dessert mille-feuilles con pomodorini del Piennolo with candied cherry tomatoes and a light lemon cream.
Millefoglie al Marzemino: a 'drunken' cow's milk cheese from the Veneto, into which a hole is bored and Marzemino di Refrontolo passito wine is inserted and swirled around, making a nice boozy cheese. Also see ubriaco.
Image by Fugzu