Roughly analogous to what would be a preliminary hearing in a civilian court, an Article 32 hearing was often the first step in determining if sufficient evidence existed to warrant recommending court martial proceedings against a member of Starfleet.
Such hearings were led by a presiding officer, who weighed the evidence and testimony of witnesses presented before making a recommendation to Starfleet. Starfleet was not bound by the officer's recommendations but usually followed them.
In 2387 an Article 32 hearing was convened on Earth to determine if Captain Jean-Luc Picard should face court martial for his role in forcing Min Zife from the office of Federation President. After reviewing evidence and testimony, Admiral Marin Liu decided against recommending court martial for Picard, but did enter a reprimand in Picard's service record that ended any possibility for further promotion to that of Flag officer. (TNG novel: Collateral Damage).