It's a bit tongue-in-cheek. Irish Medieval folklore like the Lebor Gabála Érenn (usually known as the Book of Invasions in English) attempted to provide an extensive past history for the Irish people and their island, with a heavy Christian influence, positing that Ireland was settled in several waves of invasions, the last of which, the Gaels are supposedly descended from Adam via Noah and his son Japheth, with Fénius Farsaid - one of the architects of the Tower of Babel - being the founder of the race (race being used in the older sense of "lineage").

This is a bit "all in their heads" of course; the Irish were trying to square their national origins and native mythology with the Bible, which was taken as given truth. This kind of mythology-laden pseudo-history was relatively common, was more or less influential. Compare Scottish myths about being founded by the daughter of a Pharaoh, or British myths about being founded Brutus of Troy. As described in Israelites in Erin: Exodus, Revolution, and the Irish Revival 32:

In medieval Ireland, comparisons between St. Patrick and Moses, between Gaelic law and the Ten Commandments, between Irish and Hebrew, were common, and they implied a link of direct descent.

A fair bit of history and archaeology in the 19th and 20th century has been about deconstructing some of these national myths, questioning sources and the like. The Lebor Gabála Érenn isn't considered history anymore, although some of its suppositions (like the island being settled in waves of invasions, and Gaelic ancestors of the modern Irish arriving via Iberia) may have some basis in fact.

I will have to slightly disagree with u/AncientHistory that the ref is tongue-in-cheek and nor is it, as far as I can see, referring to the Lebor Gabála Érenn.

Not that I am defending Cahill in any way - the book has some very serious flaws and was badly reviewed by Irish scholars in Ireland. I looked up my copy of Cahill's book and see that the ref you quote is actually from a footnote which he begins by a ref to Conchobar Mac Nessa and the lineage of the O'Connors. This is from the Ulster Cycle of mythology which lays out the story of Conchobar and leads into the great Irish epic the Táin Bó Cúailnge - [the Cattle Raid of Cooley]. This epic - and its antecedents - make up the oldest mythology written in a vernacular western European language. This alone makes them significant.

The problem is that Cahill seems to take these texts as actual history and treats them as such within his text. Hence he regards the lineage of the O'Connors as fixed by this ancient text . This is the wider problem with How the Irish Saved because Cahill appears to take much of Irish mythology as history or certainly treats it as such. His appears to lack any knowledge of Irish archaeology.

The same goes for his treatment of St Patrick - he takes the frankly propaganda texts of Muirchu and Tierchan on the life of Patrick and accepts them at face value. Cahill makes no distinction between these stories and what we do actually know of Patrick. Muirchu was actually writing to establish Patrick as the hero and founder of Irish Christianity [he did succeed in this] and to likewise establish Armagh as the primacy [he succeeded in this also]. But his work is almost pure fiction.