I haven't had much luck finding a side-by-side comparison but I hope this[1] image helps me explain it better. You can see the fabric's grainline where the thread is pulled loose. If you imagine the loose thread is a seam you can (sort of) see the other threads of the fabric run either parallel or perpendicular to it.
Now instead imagine the seam is at the raw edge at the top of the photo. Do you see how the pulled thread of the grainline isn't parallel and will eventually intersect with the line of the (imaginary) seam?
Edit: The inset of this[2] image might help as well. See how the lines marked "warp threads" run parallel to the selvage and the "weft threads" run into the seam at a 90 degree angle? The threads should intersect the primary vertical seam of a garment the same way.
