GLX texture from pixmap is an extension that can be used to create an OpenGL texture from the contents of a X11 pixmap (such as the contents of an application window). This functionality is required to efficiently use OpenGL to render window contents to the screen (the alternative being to suck the pixel data into the window manager and then create a texture manually).
GL npot or rect textures refers to the ability to create textures of arbitrary dimensions. Earlier graphics hardware could only work with square textures whose dimensions were a power of two (e.g. 2, 4, 8, 16, 32, etc). The
npot part stands for "non power of two". If you are dealing with window contents as textures, this is pretty important.
GL vertex program and
GL fragment program are extensions used to program parts of the OpenGL pipeline.
GL framebuffer object is an extension to allow off screen rendering. Traditionally OpenGL operations render directly to the screen. Rendering off screen allows the resulting image to be processed further (e.g. used to create a texture for further rendering.
GL version is 1.4+ is just checking what version of OpenGL the driver claims to support. This check would be to determine whether the driver supports a minimum baseline of functionality required by that version of the specification.