Graphics and video
For a list of games, see games with high dynamic range support.
High-dynamic-range rendering (HDRR, HDR rendering or high-dynamic-range lighting), is the process of generating computer graphics scenes using lighting calculations done in high dynamic range (HDR). This allows preservation of details that may be lost due to limiting contrast ratios, by mimicking the way cameras and even eyes handle light exposure. It is especially helpful when rendering scenes with multi-layer surfaces, especially when the surface is using normal and specular maps or even highly reflective surfaces (like the water), which can not be rendered correctly in Standard Dynamic Range. 
Another important area where HDRR is useful are exceptionally dark and exceptionally bright areas as well as transitions between them. Using a dynamic tone-mapping, HDRR can adjust the exposure of a scene based on the amount of light in it to simulate a camera lens adjusting to the light. But the games rendering in HDR don't necessarily output that image in HDR Display compatible range. Due to technical limitations they had to map that vastly bigger dynamic range back onto what consumer displays commonly support. Since the introduction of HDR displays this is theoretically not necessary anymore.
High Dynamic Range output or High Dynamic Range is a technology that first and foremost enables a screen to display an image at a much greater range of contrast. In practice this usually goes hand in hand with an increased color bit depth from standard 8-bits per color to 10-bits per color or more. In any case, both the software, graphics card (incl. driver), connection and display need to support this technology in order to actually be able to put a HDR image onto a HDR display.
According to the Ultra HD Alliance's UHD Premium certification, HDR displays must have either a peak brightness of over 1000 cd/m² and a black level less than 0.05 cd/m2 (a contrast ratio of at least 20,000:1) or a peak brightness of over 540 cd/m² and a black level less than 0.0005 cd/m² (a contrast ratio of at least 1,080,000:1).
More recently VESA has published a certification of its own, called DisplayHDR, breaking the market down into 3 segments of 400, 600 and 1000cd/m² required max brightness by the display among other details.