Short answers, pulled from the story.
The Tudor rose is the traditional heraldic floral emblem of England. It consists of five white inner petals representing the House of York and five red outer petals representing the House of Lancaster, symbolising the union of the two rival dynasties after Henry VII married Elizabeth of York in January 1486.
The Tudor rose was created after the Battle of Bosworth Field in 1485, when Henry VII took the crown from Richard III. Historian Thomas Penn argues the red Lancastrian rose barely existed before Henry VII, who invented the combined red-and-white emblem to project himself as a peacemaker king after the civil conflicts of the 15th century.
The Tudor rose is most often depicted as a double rose with white petals on top of red, and is described heraldically as "proper," meaning naturally coloured. It could also appear slipped and crowned, showing a cutting with stem and leaves beneath a crown, or dimidiated, meaning split and joined with half of another badge.
The Tudor rose appears on the dress uniforms of the Yeomen Warders at the Tower of London, the royal coat of arms of the United Kingdom, the coat of arms of Canada, and the badge of the Supreme Court of the United Kingdom. It was also on the British 20-pence coin minted between 1982 and 2008, and on the heraldic badge of HMS Queen Elizabeth, the Royal Navy's current flagship aircraft carrier.
York, South Carolina is nicknamed The White Rose City and Lancaster, South Carolina is nicknamed The Red Rose City, reflecting the names of the English cities and their respective heraldic roses. York, Pennsylvania and Lancaster, Pennsylvania carry the same nicknames. The borough of Queens in New York City uses a Tudor rose on its flag and seal, and Annapolis, Maryland displays a Tudor rose on its flag and seal alongside a thistle.
The slipped and crowned form of the Tudor rose, showing a stem and leaves beneath a crown, became England's royal floral emblem by an Order in Council dated the 5th of November 1800. It fulfils the same role as the thistle for Scotland, the leek for Wales, and the shamrock for Ireland.