Why (specificaly) would a patient with copd breath better when he or she is in a sitting position?

Leverage: In COPD you need to make a bigger effort to breathe, to compensate for the narrowed bronchial tubes. This is generated by the breathing muscles which are located between the ribs, in the neck area, and upper torso. The muscles generate the most force when they are not too stretched and not too relaxed. This is best achieved in the seated position. Other factors also play a role.

Gravity: When you are sitting, gravity helps the breathing muscle called the diaphragm pull down and open up your lungs to let the air in.

See below: The abdominal contents do not push on the chest and allow for the lungs to expand better, as opposed to lying down. When upright, there is more energy expenditure especially if walking or doing other activities.