if it is not straight (on-grain) it is bias...and very stretchy...
your edges will lie flat if your pieces are cut straight. if you cut off grain your pieces easily stretch out of shape. also if you fabric is not folded on the straight grain and you cut a strip you get those little V's in your strip at the fold....patterns (including clothing and other sewing) often have a line/arrow showing which direction the pattern piece should be placed on the fabric ensuring it is situated correctly (on-grain) things do not (hang/drape) correctly if cut incorrectly
if you want your borders straight, if you want your quilt to be square, if you want it to drape evenly...it is important to cut correctly--on grain