Non-juror and jury come of course from the same root, the late Latin word "jurat" = oath.
A juror swears an oath to "well and truly try this case and a true verdict render according to the evidence, so help me God."
The non-juring Episcopalians refused to swear the Oath of Allegiance to William and Mary. The non-juring Episcopalians in Scotland also refused to submit to the Established Church (Presbyterian). So there's still an independent Episcopal church in Scotland (although it's very very small). After the American Revolution, when the Anglicans in America needed a bishop the English bishops refused to consecrate him because he couldn't take the Oath of Allegiance to the king. So Samuel Seabury went to Scotland and was consecrated there, and that's why American Anglicans are known as Episcopalians.
Interesting (well, if you're a trivia nut) factoid: Rev. Robert Kirk of Balquidder, who wrote the book The Secret Commonwealth about the Good Folk of Scotland, was a non-juring Episcopal minister.
Thanks for your enlightenment.