A QR Code (short for "Quick Response") is a barcode that contains data that can be read by a phone's camera.
Most smartphones come equipped with an app that can scan QR codes. Or you can download a QR code reader from a variety of places--most are free. Once you open the QR code scanner app (or reader as they are sometimes called), the phone's camera acts like a scanner, allowing it to "read" the barcode.
These codes contain information like a website's address, personal contact information, phone number, SMS, a link to a video, etc. Think of it as a black and white link, or a heavily pixilated one.