I'm glad you asked. In my web peregrinations having to do with Italian food, I have often come upon this word in conjunction with various recipes. It was amply clear that it is some sort of device or machine.
So I did some digging and found out that the gadget is a rather expensive multi-purpose kitchen machine. Here it is.
Looks like a combination coffemaker/pie baker. Despite its popularity among Italian cooks, it's not Italian. Internationally, it's called the Thermomix and produced by Germany-based Vorwerk, although they state that the appliance itself "started" in France in 1971. The name "Bimby" probably appeals to Italian ladies because of its association with bimbo (baby, little kid.)
The little Franco-German kid is now apparently available in the US, according to their site. A cursory spin around the Internet brought me to the conclusion that the machine will cost you over a thousand dollars. But they maintain that it is not a food processor and does practically everything in one place. Easy clean-up, too. As I will neither be buying one or using one, I suggest that you use keywords "ricette Bimby" or a specific recipe name in Italian plus "Bimby." If you don't know Italian, try your luck with instant translation (at your risk.)