Because "nuair" is actually a contraction of ΅an uair", meaning "the hour" or "the time". It's grammatically speaking a noun, not a conjunction. You need an actual conjunction in there to introduce the relative clause, which is "a". "A" here is the relative pronoun that connects the following phrase to the rest of the sentence. "A" as a relative pronoun can mean "who", "which" or "that" depending on the context. The whole phrase is "an uair a/nuair a"--this more or less means "the hour/time that (something happened or happens)" and it is commonly translated as "when" in English. Hopes that's not too confusing. Isn't Irish fun? :)
Thank you! I thought it was a formal conjunction. So, should I always use "a" after "nuair"? I am not quite sure, but I think I remember some excercises in the course where "nuair" was alone, but perhaps it was valid due the particular structure of the phrase. And yes, Irish is very funny and beautiful. I am having a great time trying to learn, though I am not sure how well I am doing, but it will not discourage me. I have found a particular beauty in the "prepositional" perspective of the language for things that have particular verbs in other languages I know.