Similar to the French millefeuille 'thousand sheets', in Italy the word usually refers to puff pastry 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.
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