Augmented reality is the technology of overlaying computer generated imagery on top of what is already visible in the real world. It can be seen on a TV, phone, tablet, or even projected onto a headset. The important part is that it allows users to view information while still being able to see the world around them.
Augmented Reality - (noun) an enhanced version of reality created by the use of technology to overlay digital information on an image of something. - Merriam Webster
Virtual reality is when the entirety of one's surroundings are generated by a computer. VR involves a headset that completely obscures one's view, allowing the entirety of one's vision to be filled by a simulation. Examples include the HTC Vive, Oculus Rift, Google Cardboard, and Playstation VR.
Augmented reality is when one's surroundings are supplemented, or augmented, by computer imagery. The entire point of AR is that it does not obscure one's view, instead providing them with relevant information while allowing immersion in the real world.
For many people, their first encounter with AR was on September 27th, 1998, when ESPN and Sportvision introduced the yellow first down line for football games, generated with AR technology.
Unlike virtual reality, augmented reality technology is not limited to overhead headsets. Any time a computer is drawing imagery on top of the real world, that's AR. Everything from the graphics during a sports broadcast viewed on TV, such as the NFL's iconic first down line, to videos seen on a phone, such as Snapchat's filters or Pokemon Go, and everything inbetween are all classified as augmented reality. AR is everywhere. For more examples, see the uses page.