According to health experts itchy palms may be a sign of diabetes type II or chilblains depending on its severity. They however recommend one to visit a dentist for diagnosis. The myth behind itchy palms however, is you will get money if it is your right hand itching or you will give out money if it is the left palm.
1 Additional Answer
It is a traditional saying that: If the palm of your right hand itches, it betokens that you are going to receive money.