Princess Royal is a title often given by the reigning British King or Queen to his or her eldest daughter. The title is a gift of the monarch, unlike Prince of Wales which is always given to the eldest son
There can only be one Princess Royal at a time, so Elizabeth II never held the title because her aunt, Princess Mary was already called Princess Royal.
List of Princesses Royal
The following is a full list of women officially called "Princess Royal":
Princess Louisa Maria (1692–1712), the last daughter of King James II (d. 1701), was born after he lost his crown in the Glorious Revolution. She was given the title of Princess Royal during James's exile at Saint-Germain-en-Laye and was so called by Jacobites, even though she was never even James's eldest living daughter.
Eldest daughters of English sovereigns
Before Charles II in 1660 started using the title of Princess Royal, the eldest daughters of the King of England had a special status. The Magna Carta made the Barons to pay for the eldest daughter's wedding, and later sleeping with her was made High Treason, punishable by death - a law only changed in 1998