Augmented reality is a type of program that shows graphics rendered onto a real life scene. This is done by using a devices camera in real time (such as on a phone or webcam), and using compatible images (or in some cases rendering directly onto the scene) the software can recognize.
This then tells the application to render either a 3d or 2d graphic on top of the image placed. through the screen on the device, it now displays the object on the scene.
Augmented reality is sometimes mixed up with virtual reality. While augmented reality is about displaying rendered objects onto a real life space, virtual reality is about simulating a virtual space.
This is usually done through the use of specialized hardware (such as a VR headset). *However has simpler alternatives that make use of a phone and a housing for the phone.
In simple terms, mixed reality is a combination of both virtual and augmented reality. Taking the ability to display objects onto the environment from augmented reality, however integrates itself with the virtual spaces of virtual reality. As well as allows virtual and physical objects to also interact with each other (examples below of how this works).
(Example One: You could have a ball in real life, and mixed reality could interpret the ball to render as a rock in the MR headset)
(Example Two: You could have a ball in real life, and you could throw it at a virtual stack of boxes and the ball would knock them over.)