HDR stands for High Dynamic Range. The purpose of HDR technology is to compensate for high contrast lighting issues (i.e. really bright areas and really dark areas in the same scene). The difference between the brightest section and the darkest section of the scene is referred to as the dynamic range.
Cameras with this feature use a special HDR software to help balance these differences. A typical example of when this technology is especially useful can be usually found when using a security camera indoors. On one hand, the inside of the building will be appropriately exposed, but on the other hand, a window in the background will be completely over-exposed (or vice-versa - the camera will be able to see slight details outside, but the interior will be too dark).
The HDR feature will try to compensate for this to allow for some visual details outside without affecting the interior lighting. It does this by creating different exposures - over-exposed and under-exposed. It will then combine these exposures to balance the lighting in both areas.