What does this mean?

Naomh is Saint and I believe Nais is short for National (náisiúnta in Irish) and Aine possibly a diminutive for Andrew (Aindréas) or the old Irish goddess Áine ?, this would make the English equivilent - St. Andrew's National School ... unless there's a Saint Áine ?

the link to Wikipedia for Áine will not appear for some reason - if you google Wikipedia and the name it shows up ok.. 

sorry - second thoughts...I think it might be St Ann(e) - Áine  .. the Fada might be important

does this reference relate to a specific school ?

(there are quite a few Schools named St. Anne and St. Andrew)

The School at Maio (Trohanny townland), County Meath is St Anne's National School, so at least that answers the Ann/Andrew question..

No sign of a school on the earlier OSI maps c1840 but there was a school in the area shown on the 1890s OSI map marked as 'Maio School' see attached OSI map extract. It's not on the same site as the current school, the site currently seems to the grounds of a modern house, no sign of any ruins that I can see on the map or aerial view - it is however just a short distance between the two locations, less than 1km between the current school and the site of the older school. See the attached Google map view.

The current St. Anne's School is on a site where there were no buildings are shown on the historic OSI maps (1890, 1840), based on later maps it was built sometime after c1935, but before 1995..

There are essays written by pupils at the old Maio School in the Duchas Collection, you can scroll through the handwritten pages to see the full details