Each vertex of model have its coordinates in 3d space + it have its coordinates in texture space ..its caled UV coordinates.
Texture space is only 2d with U=0, V=0 in upper left corner of texture and U=1, V=1 in bottom right corner. Means that regardles on pixel size, texture have allways size of 1,1. Even texture of 256/128 pixels is 1,1 big.
U is horizontal coordinate while V is vertical.
To edit UV coords of model there are editors called UV editors. Most of modeling progs. have one built in. There are also pure UV editors. You can download one freeware one on my site. Its called LithUnwrap and its one of the best.
Another freeware one is here: http://www.uvmapper.com/
but I have no experience with this one.
Bye the way from what you described I think that simple plane (box) would serve you better than cube since you need only top side of it.