HDR or HDRI refers to techniques and images that are capable of taking or showing higher dynamic range as usual photography and imaging. True HDR images use a higher bit depth and/or floating point format in order to extend the range of values. There are several HDR formats among them
- .hdr Radiance format
- .tif Floating point TIFF
- .pfm Portable floatmap
- .float Raw binary floating point
- .exr OpenEXR format
Some more info on HDR is found on wikipedia: 
HDR is used more or less accurately for almost any way to get more details out of the shadows and/or highlights. True HDR is only possible by Contrast Blending (see there for details) or specialised equipment like HDR cameras (f.e. SpheroCamHDR) or HDR Monitors.