A prince is a title usually given to a son of the king. A female equivalent is a princess.
Although there are usually no princes amongst the wizardkind, there was at least one princess who was a witch; this was Mary, daughter of Henry VIII, who became Queen of England, Ireland and Spain. Her half-sister, Princess Elizabeth, never married, but became queen, too.
Although there are usually no princes in the wizarding world, there are persons surnamed like that. There is a Prince family. The only known family member, Eileen Prince, married a Muggle and had a half-blood son, Severus Snape, who was known as The Half-Blood Prince.
Prince is a general term for a monarch or a member of a monarch's family, and is a hereditary title of some European royalty, likely alluding to the aristocratic status of pure-blood families in the wizarding world. The word is derived from the Latin princeps, meaning "first", which was one of the titles of the Roman Emperor, in which case it was generally translated as "First Citizen". The Prince is also the title of a famous political treatise by Niccolò Machiavelli; an interesting point considering that the adjective derived from the author's surname, Machiavellian, is defined as "attempting to achieve goals by cunning, scheming and unscrupulous methods", which may allude to the ideal traits of Slytherin house.