(covers information from several alternate timelines)
The manual steering column was a helm control option aboard some spacecraft that resembled a joystick. It was capable of providing fine piloting control in situations where the normal helm controls were not precise enough.
The Sovereign-class USS Enterprise-E had a manual steering column that allowed the conn to manually control helm functions if the need arose. Commander Riker utilized the column when performing precise maneuvers inside the Briar Patch to collect metreon gas with the ship's ramscoops and subsequently release it in the vicinity of two Son'a battle cruisers. (Star Trek: Insurrection)
The second Delta Flyer used two manual steering columns in her helm configuration, having them almost completely replacing the old manual steering columns that had been used on the previous Delta Flyer. (VOY: "Drive")