I understand why the Glorious Revolution happened, but don't understand why William of Orange was asked to become King of England. What was his claim or connection?
William was the husband of Mary aka the eldest Daughter of James II.
William III (William of Orange) was a grandson of Charles I of England through his daughter Mary, the Princess Royal who married another William of Orange. In this way, he had a double claim on the throne because he, himself, was descended from the Stuart line and he was also married to his first cousin, Mary (Mary II of England) who was the eldest daughter of the deposed James VII/II.
The line of descent is as follows:
Charles I married Henriette Marie de France and together they had: