It probably developed in ancient Greece & Rome, moving from there east to China, Japan, & India, and north to France & England. It is reported that the sport was sometimes called shuttlefeather, although I cannot find reference to this in the Oxford English Dictionary.
Players used a paddle, called a battledore, to keep a cork stuffed with feathers, called a shuttlecock, in the air for as long as possible. The battledore was a small, lightweight racket made of parchment or rows of gut stretched across wooden frames. Battledore was originally the name given to a wooden bat used for beating clothes during washing in England.
Battledore makers used leaves of old and sometimes valuable books to cover their rackets. A 1792 story in The Federal Gazette and Philadelphia Evening Post related that "A page of the Second Decade of Livy was found by a man of letters on the parchment of his battledore, as he was amusing himself in the country. He ran directly to the maker of the battledore; but arrived too late; the man had finished the last page of Livy in compleating a large order for these articles about a week before."
Because the shuttlecock was a feathered projectile, its inherent aerodynamic properties made it fly through the air differently than the more ordinary balls used in most racquet sports. The feathers created higher drag, causing the shuttlecock to decelerate more rapidly than a ball. On the other hand, shuttlecocks had a higher top speed compared to balls in similar racquet sports, so shuttlecocks could be a little tricky to control. Since shuttlecock flight could usually affected by wind (because of its lightness), the game was sometimes played indoors. It was usually played outdoors during warm weather as a casual recreational activity, often in private & commercial pleasure gardens. By the 16th century, it had become widely popular among children in England. In Europe this racquet sport was known as Jeu de Volant and was popular with the upper classes. The game traveled to the British American colonies with the English settlers.
At the Maryland Historical Society in Baltimore, documents survive of a 1742 order of battledores & shuttlecocks sent to Maryland from an English merchant. American gentry began to have portraits of their sons painted with their bright red battledores and shuttlecocks, the spelling of which varied across the years.
In 1764, the Boston Gazette and Country Journal carried an advertisement selling imported "Battledores and Shittlecocks." And in 1770, the Boston News-Letter advertised the sale of "Battledores and Shutlecocks." The 1782 Royal Gazette in New York City offered "Battledores and Shuttlecocks For the Season," as did the New York Packet and the The Pennsylvania Packet and Daily Advertiser in 1790. An 1831 notice in the Baltimore Patriot advertised for sale "Battlecocks and Birds."
1758 John Singleton Copley (American colonial era painter, 1738-1815). Young Thomas Aston Coffin with Battledore and Shuttlecock.
Battledore and shuttlecock was not a competitive sport. Probably the most intriguing aspect of the game was that it was a cooperative sport with the players trying to see how long they could keep the shuttlecock in the air. It did not pit player against player, a rather refreshing concept in the 21st century. The game was usually played by children, families, and young adults during the 18th century.
During the 19th century, American girls were encouraged to play battledore and shuttlecock to maintain good health. In 1828, Republican Star and General Advertiser of Easton, Maryland, published an article on Exercises Most Conducive to Health in Girls & Young Women. "Nearly the same exercises with the exception of wrestling, cricket, quoits, & those sports properly termed athletic, which are proper for boys, may be recommeded for young girls--trundling a hoop, battledore, trap ball, and every game which can exercise both legs and arms, and at the same time the muscles of the body, should be encouraged."
Battledore & Shuttlecock Portrait of a Boy, c.1758-1760, by John Singleton Copley
1770-75 William Williams (American Colonial era painter, 1727-1791). Portrait of Master Stephen Crossfield
1787 Shuttlecock A Little Pretty Pocket-Book, Intended for the Instruction and Amusement of Little Master Tommy, and Pretty Miss Poll” by Isaiah Thomas, Worcester, Massachusetts