It says 'daonra na hÉireann' - when you have an article before a genitive noun like that, it mean the whole noun phrase it's part of is definite. The construction 'X an/na Y', where 'Y' is a genitive noun, means 'the X of Y'.
It's a bit of an unusual feature of the language. This construction occurs in the semitic languages too. For instance, in Arabic, you'll see things like 'X al-Y' ('al' being the definite article in Arabic), and that translates as 'the X of Y'. This is more-or-less the same construction as in Irish.
Some people have attested, on grounds of that, word order, the broad-slender thing and probably other reasons, that there is a large Semitic influence in the Insular Celtic languages.
I've heard that too, but I doubt it strongly. Also, the broad-slender contrast doesn't occur in Semitic languages, so you might've been thinking of Slavic languages there, where the hard-soft contrast is quite similar to the one in the Goidelic languages (Irish, Manx, and Scottish Gaelic).
The Celtic languages really aren't that odd as languages with VSO word order go. Their weirdness is mainly phonological, and even with this, we have a good idea of what caused it through historical linguistics (lenition being generally a loss of final -s in the preceding word and eclipsis being a loss of final nasals in the preceding word).
The only thing that occur in the Celtic languages and the Semitic languages are the VSO word order and how definite genitive noun phrases are formed, but even these can be explained by using language universals (universal trends how languages with certain trends will pretty consistently tend to have others).
Moreover, we have pretty solid historical evidence that the Celtic languages largely (with the exception of Gaulish) had VSO word order long before contact with any Semitic peoples, the Phoenicians in particular, could plausibly have happened.
The enduring myth of a link between the Celtic peoples and the Phoenicians primarily comes from the time before Irish and the other Celtic languages were solidly established as Indo-European, because they seems so different from the typical Indo-European language. In truth, there isn't a tonne of native vocabulary that can't be traced back to PIE somehow, and what can't be doesn't appear to have a Semitic origin either.
Now, none of that is to say that there wasn't contact, just that its effect on the languages is often overblown. There was almost certainly trade between Carthage and Ireland and Britain, but none of that would be enough to drastically affect the typology a language family spanning from the Iberian peninsula to Dunnet Head in Scotland.
Your sentence is ambiguous. If you were talking about the demographics of a city like London, for example, you could ask "What is the Irish population?" meaning how many Irish people live in London, in which case Cad é daonra na nÉireannach? would probably be more appropriate.
Translating daonra na hÉireann as "the population of Ireland" or "Ireland's population" avoids this ambiguity.