Wifi is just a wireless Internet signal, normally created by attaching a wifi router to a wired ISP connection, so that you can access the Internet wirelessly on your laptop or mobile devices. It is certainly useful, cheap and extremely widespread.
WiDi is a proprietary Intel tech, Wireless Display. It allows one to wirelessly broadcast your laptop display on your TV. It requires a special CPU, wifi card in your laptop, a special widi receiver (like Netgear PTV1000) and free download software from Intel. It is fun, But expensive, and in my opinion, relatively unsuccessful.