De la Enciclopedia Cecilia
According to their website: "Ceili" (say: KAY-lee) is a Gaelic (Irish) word that means "party," specifically one with live musicians, dancing and general merriment. "Coeli" is a form of the Latin word for "heaven." Rain is that stuff that falls from the sky. Thus, Ceili Rain is a "downpour of heavenly partiness."