A scepter is a ceremonial staff, often used by kings. With its jewels and ornamentation, a scepter is a symbol of power.
Scepter is related to a Greek verb that means to prop oneself or lean on something. That makes sense, since a scepter is something a ruler can lean on, like any other staff. However, you won't find an ordinary citizen with a scepter. If the President started carrying a scepter, people would probably get worried; it would suggest that he is thinking of himself as a king.