He goes to a concert once a month.
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In this sentence what does "a" before 'concert' mean?
Does 'a' mean 'one'? Or is 'a concert' used in generic use?
It's rather generic, but yes, it does mean "one." If he went to more than one concert a month, you'd use one of these:
He goes to at least one concert a month.
He goes to at least two concerts a month.
He goes to a couple of concerts each month.
He goes to as many concerts as he can every month.
He goes to several concerts a month.
(And there are others or you can alternate the wording of those above.)