Hand quilting usually refers to the process of securing the quilt layers together by hand stitching. Some folks also consider hand stitching patchwork together a form of hand quilting.
Quilters who prefer hand quilting the top, batting and backing together are most concerned about their stitches. These stitches will show up on both the top and back. Good hand stitches should be as consistent in size and small (more than 10 stitches to the inch); with consistency rating higher than size.
In the above photo, a one inch grid has been hand quilted. The stitch size is about 8 to every inch. (As you can see, my hand quilting is not so great!)