International Association for the Study of Pain (IASP) defines pain as “an unpleasant sensory and emotional experience associated with actual or potential tissue damage, or described in terms of such damage”. Describing pain as "unpleasant" is rather subjective, but it is acceptable to say that pain has one meaning; something is wrong!
We need to be able to feel pain because pain makes us do something about the feeling and seek help. Thanks to pain, when we touch a hot object we quickly withdraw our hands, when we have a back ache, we adjust our posture and when we have a broken leg we go to the hospital.
However, there are people who can not feel physical pain. It is a rare condition called "Congenital Analgesia" or "Congenital Insensitivity to Pain (CIP)". People who are born with this condition are prone to having injuries without being aware of it. It could be very dangerous because it could delay a person from seeking medical attention for serious injuries.