They come to us from Japan where they are very common. QR is short for Quick Response (they can be read quickly by a cell phone). They are used to take a piece of information from a transitory media and put it in to your cell phone. You may soon see QR Codes in a magazine advert, on a billboard, a web page or even on someone’s t-shirt. Once it is in your cell phone, it may give you details about that business (allowing users to search for nearby locations), or details about the person wearing the t-shirt, show you a URL which you can click to see a trailer for a movie, or it may give you a coupon which you can use in a local outlet. The reason why they are more useful than a standard barcode is that they can store (and digitally present) much more data, including url links, geo coordinates, and text. The other key feature of QR Codes is that instead of requiring a chunky hand-held scanner to scan them, many modern cell phones can scan them. The full Wikipedia description is here.
Due to the widespread use of smartphones, QR Codes are mosly used for mobile marketing purposes these days. Marketers benefit from QR Codes by being able to add digital content like websites, videos, PDFs, image galleries or contact details to printed media such as flyers, posters, catalogues and business cards