OK so HDR is High Dynamic Range imagery.
Basically it's the process of using different exposure values combined together in software so that very high contrast range scenes can be rendered on screen or print. There are some very bizarre images that can be created that way, but we're trying for something "Real as seen by the eye, rather than the camera."
The test image we shot the other day looks like a good candidate, the sun on high wispy clouds is about as 'highlight' as you can get and the brush on the far riverbank is pretty darn black.

Mary's River confluence, Canon 590IS, 37mm-eq, f8@1/400 ISO100 JPEG-Fine

Mary's River confluence, Canon 590IS, 37mm-eq, f8@1/100,1/400,1/1000 ISO100
Combined in Unified Color's HDR Photo Studio 2/64
It's arguably an improvement, the mid-tones on the beach are retained, the sky isn't as blown out and though you can't really see it at this resolution, the details of the brambles on the bank are more visible. At the same time I don't think it looks 'over-processed.'
Lens flare is accentuated somewhat, but some of the 'default over-sharpening' that the camera applies automatically is slightly reduced by the de-Halo processing step in this HDR software.
The shot still looks a little smeary due to a big nasty thumbprint that was on the front lens element. This is the first test shot(s) with the 590IS we got on eBay for 67 bucks and I hadn't checked to see if the lens was clean. How very embarrasing.
In the future we'll be Trying other HDR packages and will probably post those results.