"Merge to HDR" is a technique that takes 3 or more different exposures of the same scene, and uses them to create a 32 bit image file with a higher dynamic range than would be possible in a single exposure with the gear/media/materials. For DSLRs with a normal dynamic range of 6 stops or so it's possible to get a file with a dynamic range of 10 to 12 stops with 3 exposures bracketed at 2 stops apart.
This 32 bit file with the higher than normal dynamic range is not really viewable on most monitors or any print, because monitors and prints have a maximum displayable dynamic range of about 5 stops. To create an image that is printable, or viewable on a normal monitor, the 32 bit file is converted to a 16 or 8 bit image file, and the dynamic range/contrast is compressed using a variety of methods depending on your software.
The part of this that most people notice actually has little to do with high dynamic range. It's the appearance or manipulation of the local contrast that makes it look the way it does. It's completely possible to manipulate the heck out of the local contrast in a regular dynamic range photo, and get similar looking results. Burning and dodging, adjusting lighting ratios, the zone system, graduated ND filters, USM (in the darkroom or PS), contrast masking, tone mapping, and the various methods of converting from 32 bit HDR files are all techniques for manipulating local contrast.
BW film has a higher potential dynamic range than most other photographic media, but getting 10 to 12 stops on a BW neg is still within the normal range for a single exposure. Merge to HDR with 3+ different exposures should allow for dynamic range beyond what is possible in a single exposure. Not that we can see it all at once with current technology.
I think people like it because the photos with heavy local contrast manipulation look like paintings (ala Photomatix). Painters have been using local contrast manipulation for centuries. But just like any technique, it doesn't have to be taken that far. Local contrast can be manipulated to bring out more details in the shadows and highlights, and still look like a "normal" photograph to the viewer.