Short answers, pulled from the story.
Heraldic badges with a distinctly heraldic character first appeared in England during the reign of King Edward III from 1327 to 1377. These symbols emerged within the context of tournaments and courtly celebrations before evolving into political tools.
A coat of arms belonged exclusively to an individual, but badges could be shared among many people. Badges sometimes imitated charges found in a bearer's coat of arms or referenced them directly while more often they commemorated remarkable exploits or illustrated family alliances.
The lavish livery badge known as the Dunstable Swan Jewel dates to about 1400 AD and likely represents Henry V as Prince of Wales. Such jewels were worn only by the person whose device was represented, their family members, or important supporters.
Richard II utilized a White Hart lodged, a white falcon, a Sun in Splendor, and a Sun Clouded while Richard III adopted the White Boar and the Sun in Splendor as his personal badges. King Richard III ordered thirteen thousand badges in fustian cloth with his emblem of a white boar for his son Edward's investiture.
Heraldic badges were revived in 1906 by the College of Arms under Alfred Scott-Gatty. They have since been included in new grants of arms alongside traditional coat of arms awards.