HDR stands for High Dynamic Range. Dynamic range is the term used to refer to the total difference between the brightest part of a scene and the darkest part of a scene.
In short, a digital camera can not capture the full dynamic range of a scene in many situations. HDR is a technique that is used to overcome the limitations of the camera to capture more detail. Several images of the same scene are captured at different brightnesses and then combined to create a final image.
This over-simplified diagram should give you the idea. In this diagram the HDR arrow represents several steps and/or processes that can be collectively thought of as the HDR process.