The fact that it reduces inflation helps to reduce pain also. Inflammation is one of those things that contribute to many disease processes. So reducing inflammation not only may reduce pain but can help one to stay healthy.
Biomechanically speaking inflammation typically puts pressure on nerves or a particular nerve and causes pain.
Pain is your body telling you there's a problem. One tricky thing however is that we can have pressure on a nerve or nerves in a particular spot that doesn't detect pain. Hence you can have a disease process building and not even know it's there...
As another note, they have found that taking the turmeric with black pepper helps to activate it. Curcumin is the active component in turmeric.