"HDR" has acquired two different meanings.
Technically, it's any image with an enhanced dynamic range. Done in a subtle manner, you can't even tell it's an HDR image. Usually the trickiest part is the dark and ominous sky that often results.
The other extreme, and more common meaning of "HDR" is the whole "radioactive" look, or hand painted look, that HDR is known for. It's a fun technique and lots of folks like it. As with any fad, the novelty wore off for the most part, and now it's more of a niche thing.
Some examples:
Over the top, full blow in your face HDR:
http://www.pnwphotos.com/forum/showthread.php?t=1859
A more subtle approach:
http://www.pnwphotos.com/gallery/showphoto.php/photo/2654/title/falls-creek-falls/cat/529
Finally, an HDR with the "Foreboding Sky" effect minimized:
http://www.pnwphotos.com/gallery/sh.../snoqualmie-falls-peregrine-viewpoint/cat/504