Modifications, or ‘mods’ for short are just that – a modification and/or addition to the base gameplay in some form or fashion. There are dozens of popular mods for Quake III, all of which are made by teams of enthusiasts in their spare time. Some mods are simply gameplay tweaks and enhancements, while other mods change the game into something altogether different (Total Conversions).
Most of the well-established mods provide either an installer executable or manual zip install version (or both) for each major release. Installers are generally windows-only and usually install the mod fully after minimal input from the user.
The zip version simply contains the mod files in their proper directory structure. (pk3 files, readme files, configs, help, etc). All mods are ultimately contained in their own subfolder under your Quake3 installation folder (default is c:\program files\quake III arena). Usually the mod authors set the zip file up so that if you unzip the entire file into your Q3 folder all is set up and ready for play. You should ALWAYS make absolutely sure while extracting a zip version of any mod that you recurse the folders inside the zip (unzip while preserving directory structure). Otherwise you could be cleaning up quite the mess.
Zip versions do not create start menu shortcuts like many installer versions, so if you want to create your own shortcuts on your desktop or start menu which automatically start up Q3 with a mod loaded, add +set fs_game MODDIR to the startup command. Replace MODDIR with the foldername the mod's files are in. Best practice is to make a copy of your default Q3 shortcut and make changes to the copy.
If you wanted a shortcut to the popular OSP mod and have Q3 installed to c:\program files\quake III arena the shortcut startup command would look like this:
c:\program files\quake III arena\quake3.exe +set fs_game osp
Note: the fs_game command cannot be used while Q3 is already loaded. Use the mods menu if the game is already loaded, however the shortcut method to start most mods is recommended since many mods require other parameters, such as a higher memory allocation, also known as com_hunkmegs
Most of this information however should be documented in the particular mod's readme or help files.