The synovial joints in the fingers are called hinge joints. Hinge joints allow for movement in one plane, which is necessary for the fingers to be able to flex and extend. The ligaments and muscles surrounding the hinge joints help to keep the joints stable and prevent them from dislocating.
The synovial joints in the wrists are called ball-and-socket joints. Ball-and-socket joints allow for movement in all planes, which is necessary for the wrists to be able to bend, rotate, and extend. The ligaments and muscles surrounding the ball-and-socket joints help to keep the joints stable and prevent them from dislocating.
The combination of synovial joints, ligaments, and muscles allows piano players to have the dexterity and range of motion that they need to play music.