It allows you to draw a quad using an arbitrary part of a texture.
This is the definition of the function.
quadTexUV = function(tlx, tly, trx, try_, brx, bry, blx, bly, tlu, tlv, tru, trv, bru, brv, blu, blv)
The first two letters of the parameters indicate what corner of the quad it defines. For example tlx is "top-left x", bru is "bottom right u". So for four points you have x,y,u and v. x and y is the point's position on the layout and u,v is the texture position of a texture which are in the range of 0 to 1. Where for u 0 is the left side of the texture and 1 is the right. For v 0 is the top of the texture and 1 is the bottom.
It's basically like uv editing in 3d modeling programs except there is no z so the example you referenced isn't possible.
To use it call it in you drawgl function with glw.quadTexUV. To my knowledge there isn't a plugin that uses it yet. quadTex is used however to use a sub-rectangle of a texture. The sprite object uses it when animations are exported to spritesheets. I have also used it in my spritesheet plugin.