The na- prefix comes from the ma- prefix which denotes the ability to do something. Specifically, the na- prefix forms the completed, uncompleted and contemplated aspects of a verb that originally had the ma- prefix. Recall that the aforementioned aspects are roughly equivalent to the past, present and future tenses in English.
Thus, the verb aninag (to discern, ascertain, distinguish, figure out) in the completed aspect naaninag simply means discerned, ascertained, distinguished or figured out. In the uncompleted aspect naaaninag it means (currently in the process of) discerning, ascertaining, distinguishing or figuring something out.