In 1921 Field Marshal Douglas Haig established a charity to help former servicemen. Paper poppies were sold and people wore them in remembrance of the fallen in World War I on what was called Remembrance Day or Armistice Day. Today, the Haig Fund helps men and women who are veterans of British Armed Forces' military actions.
Poppies reminded people of the fields of Flanders in France, where so many young men fought in the Great War fought to end all wars. Here's a link that explains the American Legion's poppy program: https://www.legion.org/troops/216371/legion-family-flower-remembrance