Lots and lots of things. You are not going to get a decent diagnosis online. I strongly advise that the sufferer see a doctor if this is a chronic problem, else if it has come on suddenly then probably (PROBABLY) just keep an eye on it. The big exception to that is if the pain is accompanied by shortness of breath or chest pains. Those combined symptoms can suggest an imminent heart attack, and immediate contact with health professionals is advised (phone NHS direct, 0845-4647).
A partial list of other possibilities for the arm pain:
Pinched nerve in any arm joint, especially shoulder.
Broken bone(s)
Repetitive strain injury. RSI is an umbrella term to describe a lot of other conditions, too many to list in detail, but all related to over-use of the arm or hand.
Partial dislocation of the shoulder (or another joint)
Muscle fatigue (from ordinary exercise), strain or damage.
Ligament damage (a sprain) in any joint of the arm.
Allergic reactions (something the skin of the arm was exposed to).
Congenital deformity.
A partial list of other possibilities for the arm pain:
Pinched nerve in any arm joint, especially shoulder.
Broken bone(s)
Repetitive strain injury. RSI is an umbrella term to describe a lot of other conditions, too many to list in detail, but all related to over-use of the arm or hand.
Partial dislocation of the shoulder (or another joint)
Muscle fatigue (from ordinary exercise), strain or damage.
Ligament damage (a sprain) in any joint of the arm.
Allergic reactions (something the skin of the arm was exposed to).
Congenital deformity.