Featured in the book Quidditch Through the Ages and the subject of Irish ballads, in order to win the participant must hit the Dom through several flaming barrels against the clock, but without setting him or herself on fire. The legendary Irish wizard Fingal the Fearless was a champion of the game (QA2).
This word may be partly derived from the Irish Gaelic word aingeal, which can mean "fire, lighted coal" as well as "angel, guardian" (Teanglann New Irish-English Dictionary).
From the Web
WizardingWorld.com (Pottermore) feature: Quidditch Through the Ages
Harry Potter Wiki: Aingingein