The House of York achieved its greatest success in England during the
Wars of the Roses, the vicious civil war that occupied England during most of the 15th Century. This was a power struggle between descendants of different sons of the 14th Century
Plantagenet king
Edward III: chiefly the Lancastrian king
Henry VI and his rival Richard, Duke of York. Richard was killed in battle, but two of his sons (
Edward IV and
Richard III) succeeded where he failed.
In the subsequent history of the Royal Family of England, the title of Duke of York came to be conferred upon the son of the reigning monarch who is second in line to the throne (the Heir Apparent, in contrast, usually receives the title Prince of Wales). It is a bit like being Vice-President of the USA: sometimes you will get the top job, but generally you won't.
The present Duke of York is Prince Andrew, second son of Elizabeth II: he married and later divorced Sarah Ferguson also know as 'Fergie'. He is a military sort of
chap and fought in the Falklands War between Britain and Argentina, but is never likely to be King of England. This is probably a good thing. The historical legacy of his predecessors as Duke of York
is not encouraging: