QR is short for Quick Response (the codes can be read quickly by a cell phone). They are used to take a piece of information from and put it in to your cell phone.
The code consists of black modules (square dots) arranged in a square pattern on a white background. They are more useful than a standard barcode as 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. QR Codes are an incredibly useful mobile marketing tool. Simply scanning a text is way easier than typing it on a tiny on-screen keyboard. Save your visitors time and thus increase your click rates!
They are usually used in print materials to provide handy/quick links to web based content especially for mobile users.