HDR rendering
Half-Life 2: Lost Coast
High Dynamic Range rendering (HDR) simulates brightness above that which a computer monitor is capable of displaying, before downconverting to 
Standard Dynamic Range (SDR, internally referred to in Source and Source 2 as LDR, for Low Dynamic Range) video. This mainly involves "blooming" colors above 100% brightness into neighboring areas and adjusting a virtual camera aperture to compensate for any over-exposure that results.
Besides the obvious effects of this (see right), HDR gives richer colors and finer gradients: since bright and dark areas are pushed into white and black, correctly exposed areas are drawn with a far wider range of values.
HDR in Source
HDR rendering is first introduced with Half-Life 2: Lost Coast, and later available with 
Source 2006 and later, and requires DirectX 9 (dxlevel 90 or higher) level GPU for Windows (or OpenGL 1.4 and later for macOS/Linux).
Even through HDR was introduced in Source 2006, initially in certain games such as 
Counter-Strike: Source, 
Half-Life 2 (both at the time were upgraded to Source 2006), all or some maps weren't compiled with HDR support until the engine (and Mac) update in 2010, upgrading it to 
Source 2009 along with changes to the maps and skybox textures to support HDR.
However, as of today (with both CSS and HL2 are running on Source 2013), Valve forgot to compile all the maps with both LDR and HDR support in Half-Life 2, leaving some of the maps LDR only, and others HDR only, requiring users to enable HDR , otherwise the HDR-only map will be rendered in fullbright.
Additionally, Source 2007 improves HDR by remade HDR tonemapping in order to better fits outdoor scenes. This may results in brighter or darker image, if tonemapping was not adjusted.
Since 
Left 4 Dead engine branch and later games (with some exceptions), HDR rendering is now required and LDR/SDR rendering has been deprecated, with the option to disable HDR removed.
Note:Third-party games like 
Team Fortress 2 Classic also require HDRLimitations
Source does not have a physically accurate HDR simulation. Its camera has a far wider range than the human eye (let alone real cameras), and it also adjusts to changes in brightness far faster. Both of these are expedient to gameplay of course, especially in multiplayer.
In fact, by default, Source does not even create "proper" HDR images, and does not support native HDR output for HDR-capable TV/monitors. Instead, it collapses the image down to SDR early, like many other games in the 2000s/early 2010s. The only Source engine game that support native HDR output is Apex Legends on consoles, and it requires HDR-capable TV/monitors.
The average user would be hard-pressed to tell the difference, however, and the benefits include support for all DX9+ GPUs, MSAA compatibility, and excellent performance.
Despite LDR being deprecated since Left 4 Dead, some games like 
Portal 2 aswell as the original release of 
Dota 2 allows users to disable HDR through console commands, however:
- In Portal 2, while you can disable HDR using console command (
mat_hdr_level 0), all Portal 2 maps do not have LDR lighting compiled by default, which will cause "mat_fullbright" ('full bright' lighting) to be enabled. - In the original release of Dota 2, the game only uses LDR lighting, and none of the maps appear to have HDR lighting data. Additionally the game does not have an option to enable HDR aside from using console command.
- In Left 4 Dead HDR can be disabled via the Launch command (
mat_hdr_level 0) as it is disabled in game.
HDR in Source 2
improve HDR?
Counter-Strike 2 adds a option for switching between Performance and Quality HDR.