"....the rosette on Harry’s chest kept squeaking their names: 'Troy - Mullet - Moran!'"
-- Irish team souvenir, 1994 Quidditch World Cup (GF8)
The luminous, squealing rosettes are enchanted colourful badges of ribbon, worn to show support for your Quidditch team. The rosettes shout the names of the players until the charm wears off during the next day or so (GF7, GF8).
Ron, Charlie, Bill and Ginny Weasley, and Harry Potter all bought Ireland National Team rosettes at the 1994 Quidditch World Cup (GF7, GF8).
Seamus Finnegan had also bought one, which was still weakly saying the names of the players on the train to Hogwarts. He eventually pinned it up next to his bed (GF11, GF12).
Notes and interesting facts
Non-magical rosettes were also worn by students (and Hagrid) to support their House Quidditch team at Hogwarts (PA15, OP19, HBP4).
Lexicon timeline of Quidditch
Lexicon list of World Quidditch teams
From the Web
Writing by J K Rowling on Imgur (Daily Prophet coverage of the 2014 Quidditch World Cup, originally from Pottermore):
MuggleNet: The Best Moments of the Quidditch World Cup
Harry Potter Wiki: Quidditch World Cup
Tags: badge fans noisy Quidditch history supporter tournaments