Just to provide the absolute scantest of background detail, since this might be an obscure topic for many, the Uí Néill were a dynasty founded by Niall Naoighiallach, better known Niall of the Nine-Hostages (Though his name was more likely Nél, but the language and pronunciation changed over time), a historical King of Tara. His epithet comes from the concept of holding hostages from many septs, which represented his power and influence. The Uí Néills had an enormous effect on Ireland for hundreds of years, and were divided between two separate geographical dynasties, the Northern and Southern Uí Néills, which alternated the High-Kingship of Ireland between them.

The High-King of Ireland was not perhaps quite the figure that is conjured by the imagination from such a title, though a proper medievalist would have to get into the specifics of political structure of the period. The title itself was linked to the Kingship of Teamhair or Tara (an Anglicization I've never understood), today located in County Meath.

Tara was a sacred burial site that far, far predated the Uí Néills however, and Celtic culture in general. Though it was later that the concept of sacral Kingship, which entailed a sort of symbolic intercourse with a Goddess figure ...which is a whole other topic... came to be associated with the site.

The development of an association of Tara with sacral Kingship did not begin with the Uí Néills but it definitely was popularized by them, and they used the site as representation of their dominion over the Boyne Valley, and then Ireland as a whole.

Unfortunately I'm woefully ignorant about the political history of this period, so I'm eagerly awaiting responses as much as you are, since it's a very rich and romantic period in myths and legends - which is surely telling of an equally fascinating historical account.