Why do you have to cut the backing of a quilt bigger than the patchwork?

Look at a finished quilt. See how the quilting stitches are indented, and the unstitched parts are puffy? The stitching pulls the fabric in just a bit. This "shrinks" the fabric during the quilting process. It's even more essential when machine quilting, especially if you're quilting on a frame. With a frame, you need even more extra backing to attach to clamps. Also, whether frame, machine, or hand quilting, the more quilting stitches you have (the more detailed and complex the quilting), the more it will shrink during the stitching.

Think of it as a precaution. You'd much rather have a little fabric cut off at the end, than finish quilting and flip it over to find that your backing is a bit smaller than your top.

I'm not sure if you're also asking about how to do binding, so here's a link to binding instructions, just in case. I prefer double fold cross grain binding with mitered corners (it's in the link).

You do it because when you are quilting, it will shrink a tiny bit. You also do it just to be sure that the backing is covering the entire back of the quilt. It's easier to know if the back is totally covered when you can see the backing around the edge. It will also allow you to make a clean cut around the edges of the quilt after the quilting is done. That way you can sew on the binding without having to worry about catching all of the layers.

I also like to use the extra fabric to protect the edges of my quilt while I am quilting by folding the extra fabric over and whip stitching it in place. It prevents damage to the outer edges while the quilt is being moved around.

When you start quilting, things will start drawing up a bit. The thicker your batting, the more shrinkage you'll get. It's much easier to trim off excess than to try and figure out how to compensate when your back winds up too small.

theres always some reserve for shrinkage and displacement....(becuase batting shrinks..a good rule of thumb is at least 2 " around