"Republic of Ireland."
Translation:Poblacht na hÉireann.
This is the genitive case of Éire, and is used to signify the 'of' in the English translation. Also, it's worth noting that in native speech Éire is not used as the nominative case; native speakers would use Éirinn instead.
Standard: Tá Éire go hálainn
Natives: Tá Éirinn go hálainn
Huh thats interesting. So if i finish this course; and i went to Ireland i'ld have to relearn?
Not necessarily relearn, because most native speakers can understand the Standard. But, speaking it, you'll never be mistaken for a native.
Except the Standard isn't a dialect at all. It's a hodgepodge of actual dialects made by some person in Dublin. It pretty clearly demarcates natives and learners, since most learners never learn an actual dialect.
Éireann is the genitive form of Éire, and genitive singular feminine nouns that begin with a vowel and follow na receive a prothetic H.