Perhaps understanding why you're using an embroidery hoop will help answer the question. The hoop is going to hold the fabric taut when you are embroidering. It will also be holding the fabric in place. The pressure of a needle going in and out of the fabric can move the fabric if it is not held tightly in the hoop. The closer the hoop is holding the fabric to the the movement of the needle, the more likely the fabric is being held tightly.
On an embroidery sewing machine, the hoop moves while holding the fabric in place inside the hoop. If the fabric moves, the design that is being stitched out, will not line up and the end result will not be the desired results. Many people blame a "poorly digitized design" rather than admit there was a hopping issue when the outline does not line up with the rest of the design. Most of the time it is caused by the hoop not doing the job, not a poorly digitized design. The stabilizer you choose, as well as the size of the embroidery hoop all play a part in a machine embroidery design stitching out properly.
Whether you are hand sewing or using sewing machine embroidery, the hoop is responsible for holding an even tension on the fabric which will allow the stitches to have an even tension, preventing puckering and loose threads.
Choose an embroidery hoop that is as close to the design size as possible. Using a huge hoop for a small design is allowing more room for the fabric to move with in the hoop which leads to the design not stitching out properly. Many embroidery machines will tell you what size hoop to use when you load the design in the machine. This information is embedded in the embroidery design. Read your sewing machine manual and take advantage of lessons from local dealers to get the most from your sewing machine.
Tighten the fabric in the embroidery hoop. All embroidery hoops are adjustable to securely hold the fabric. Use the hoop adjustments to securely hold the fabric. The fabric and any stabilizer should be smooth and taut in the hoop. Do not over tighten the hoop to the point that you are warping the hoop.
The cost of embroidery hoops varies widely by the type of hoop. Machine embroidery hoops cost much more than hand embroidery hoops. Taking the time to store your hoops correctly will protect your investment. Always loosen the outer hoop tightening adjustment on any embroidery hoop to store the hoop. Tension kept on an embroidery hoop can possibly cause the hoop to warp. Store the hoops flat and away from any heat source which could warp the hoops.