Prince of Wales is the title given to the male heir to the British throne, having been insituted by King Edward I for his son, the future Edward II in the 13th century. Currently, the eldest son of Queen Elizabeth II, Prince Charles, holds the title. These days the office has no administrative function, and is purely honorific.
Usually, the wife of the Prince of Wales is titled the Princess of Wales. Prince Charles's first wife, Princess Diana, held the title from her marriage, and continued to hold it after her divorce until her death. When Prince Charles married for a second time, his new wife Camilla deliberately did not assume the title Princess of Wales, but chose instead Duchess of Cornwall, as Duke of Cornwall is one of Prince Charles's lesser titles. Female heirs to the throne traditionally have not taken the title Princess of Wales.
The name "Wales" is often used by the Prince of Wales and his family as a surname.