Augmented Reality (AR) refers to using a mobile display to impose information from the virtual world on an object you are looking at. The simplest example of augmented reality are the first-down lines put on the field during televised football games.
For the end user AR can be as simple has pointing their mobile device camera at an object and experiencing the related content on their screen. On the back end it can mean a lot of tagging of images and occasionally some programming.
This eight minute TED talk from Matt Mills and Tamara Roukaerts demonstrate some of the basics of augmented reality using an application called Aurasma. It tends towards the theatrical but does begin with an art gallery like setting.