The rotator cuff is the soft tissue in your shoulder that holds your upper arm, the humerus bone, inside the shoulder socket. When you injure or tear the rotator cuff in your shoulder, it can cause debilitating pain and keep you from doing the things you want to do for weeks or months.
Simply the weight of your own arm can cause enough resistance against the rotator cuff to cause pain, or in severe cases, either cause more damage or slow the healing process. You'll feel this pain while attempting to lift something like a glass or reaching for something.
Again, the weight of your arm can be enough to cause pain with a torn rotator cuff. Particularly acute pain can come from lowering your arm from an upraised position above your head.
Over time, either from favoring your shoulder one way or another or simply from nonuse of your shoulder, the muscles around the joint begin to atrophy, or weaken. The more they weaken, the less useful they will be over time.
Even if the pain is not particularly severe, muscle weakness can show itself either when you raise or lower your arm. You might not be able to lift things you found easy to lift before, and you could have a harder time at different positions in your range of motion than others.
Due to the tear, you might feel a crackling or moving parts type of sensation, called "crepitus," when you move your shoulder in some positions. This could be an indication that more damage is being done to the joint.