About this phrase

Bóthar is a masculine noun that means road.

Na is the genitive, singular, feminine form of the definite article, an.

Páirc is a feminine noun that means park or field. It is in the genitive case here because it is the second noun in a two-noun cluster.

Thus, bóthar na páirce: the park road (literally, 'the road of the park').

Field notes

Although páirc is commonly given in text books as the word for field, this is something of a simplification.

There is a range of Irish words for referring to specific types of field (achadh, cluain, gort, móinéar ⁊rl…). Further study is encouraged.