High Dynamic Range,
Basically, either film or sensors, have a limited dynamic range - the amount of detail that can be shown in both the highlights and the shadows. Usually if you bias exposure towards one end you lose detail at the other. HDR is a way of combining several images (usually 3 but you can use more) at different exposure settings, then combining those images in editing to produce a single image which has greater dynamic range than would otherwise be possible.
It can produce some stunning results done well. Carried too far it produces images with no appreciable highlights and too much shadow detail and it can look very unnatural - which is usually the biggest gripe of those who hate it.