A positive Murphy's sign is obtained when a patient, lying down flat on his/her back, experiences abdominal pain that increases sharply during deep inspiration while you have a hand on their abdomen, just under their right subcostal margin (under their ribs).
As the patient takes a deep breath, the diaphragm descends, pushing the liver and the gallbladder downwards. The most common cause would be, by far, an inflamed gallbladder (cholecystitis). As the inflamed gallbladder reaches the examiner's hand, the patient experiences a sharp pain and (usually) stops inhaling.
Other causes would include hepatitis, liver abscesses or even a right lower lobe pneumonia that irritates the diaphragm.