Well, let's demystify this. I am not sure why so many people are confused about the poor little quant

.
First of all, the quant is an arbitrary unit of measure (when it comes to the real world). You can make it equal an inch or a foot or a meter or whatever. It all depends on your needs. The manual recommends, for a first person shooter, that a quant equals approximately one inch or approximately 2.5 cm, but that is only a recommendation.
Now, while the quant can have an arbitrary measurement for the real worl, it has a very specific measurement for textures that is based on the pixel. One quant is exactly equal to one pixel (as long as you have not scaled your texture larger or smaller). Contrary to another post here, it does not matter if the texture is 16-bits, 8-bits, 24-bits or 32-bits. A pixel is still a pixel in size. It is just a dot. The only time the "bits" will come into play is when you want to figure out how much video memory is going to be used by that texture. No matter its bit-size, a 256 x 256 pixel texture will still take up 256 x 256 pixels.
WED, when left at its default, will have 16 quants per smaller grid square. Since a quant is exactly equal to a pixel then, by default, there are 16 pixels across the edge of the smaller square on the grid.
If you notice, there is something unusual about the grid system in WED. Instead of the standard 10 smaller blocks to form a larger grid square, there are only eight. Why? This has to do with the game engine using a power of 2 system. By having eight across at 16 pixels per smaller grid square you end up with a total of 128 quants to a major grid square (16 x 8 = 128). This means that if you made a cube the exact size as one of the major grid squares that an unscaled 128 x 128 pixel texture would fill it perfectly from edge to edge without tiling.
Basically, if you understand the quant then you can use it to properly texture your level geometry.
BTW - Textures begin their tiling (unless you shift their X and Y properties) from the world center. Therefore, if you were to create a 128 x 128 quant cube with one corner of it exactly at the world center then you could apply a 128 x 128 pixel texture to it and there would be no tiling at all. It would perfectly cover the faces of the cube (if you understand what I mean).
Well, I hope this helps.