It's the plural form of "Éireannach," which means "Irish person". The word is pronounced like "Air-in-ee".
Here's a breakdown:
* Éire means "Ireland" in Irish
* -annach is a suffix used to create adjectives and nouns denoting origin or nationality.
* -igh is the plural ending for nouns.
So, "Éireannaigh" literally means "people of Ireland".