HDR stands for High Dynamic Range. Its' a technology that can be an answer to the problem of a certain digital photography shortcoming - the limited contrast compared to the analogue technology.
If you want to shoot for HDR you have to keep in it in mind from the very beginning and plan well. You have to shoot multiple exposures (always use a tripod!), exposing for the lightest parts of the image, the darkest parts and as many midtones as you deem necessary. Its' always better to shoot more than less! By combining those exposures you will be able to extend the dynamic range of your photograph.
The best software for automatic HDR is Photomatix and Merge to HDR Pro tool in Adobe Photoshop CS5.