<p>In relation to this question on <a href="https://stackoverflow.com/questions/14413/using-opengl-extensions-on-windows">Using OpenGL extensions</a>, what's the purpose of these extension functions? Why would I want to use them? Further, are there any tradeoffs or gotchas associated with using them?</p>

The OpenGL standard allows individual vendors to provide additional functionality through extensions as new technology is created. Extensions may introduce new functions and new constants, and may relax or remove restrictions on existing OpenGL functions.
Each vendor has an alphabetic abbreviation that is used in naming their new functions and constants. For example, NVIDIA's abbreviation (NV) is used in defining their proprietary function glCombinerParameterfvNV() and their constant GL_NORMAL_MAP_NV.
It may happen that more than one vendor agrees to implement the same extended functionality. In that case, the abbreviation EXT is used. It may further happen that the Architecture Review Board "blesses" the extension. It then becomes known as a standard extension, and the abbreviation ARB is used. The first ARB extension was GL_ARB_multitexture, introduced in version 1.2.1. Following the official extension promotion path, multitexturing is no longer an optionally implemented ARB extension, but has been a part of the OpenGL core API since version 1.3.
Before using an extension a program must first determine its availability, and then obtain pointers to any new functions the extension defines. The mechanism for doing this is platform-specific and libraries such as GLEW and GLEE exist to simplify the process.