Mesa (the project itself calls it "Mesa 3D") is a free software graphics library which provides excellent driver support for Intel and AMD GPUs. Mesa has implementations for Vulkan, OpenGL and some other graphics APIs done in a way which allows most of the code to be shared and used by multiple graphics drivers. Meas has some limited support for NVidia GPUs using it's Nouveau driver; it works but it is severely limited due to NVidia's hostility towards free software and open standards in general. Mesa is written in C, C++ and there's also some assembler code for key functions.
Modern display servers like X.org and Wayland use OpenGL or EGL for all display rendering. Mesa is not only used for games like SuperTuxKart and 3D applications; all modern desktop environments and window managers use it's libraries. It is a key-stone part of GNU/Linux desktop systems, Android devices and ChromeOS machiens.