Why are William and Harry referred to as Wales?

Unlike Scotland and England, which are Kingdoms, Wales is a 'non-sovereign principality'. Traditionally, (since the 13th Century) the heir to the UK throne has been invested as 'Prince of Wales'.

Prior to the English conquest of Wales the Welsh had their own princes. Llywelyn the Great (1195-1240) proclaimed himself to be "Prince of Wales" in 1216. His son and grandson were recognised by the English kings as "Prince of Wales" until they got tired of them and decided to have them killed instead. The last Welsh "Prince of Wales" was brutally executed in 1283. Owain Glyndwr was also proclaimed "Prince of Wales" in 1400 during a brief rebellion against England... however Owain got away and may yet return to liberate his country!