(covers information from several alternate timelines)
A turboshaft, or more precisely turbolift shaft, was a passageway allowing the turbolift to move through key sections of the ship.
Kirk, Spock and McCoy were forced to climb the turboshaft of the USS Enterprise-A while attempting to escape Sybok, as the turbolifts were down. Despite the fact that Kirk and McCoy began climbing, Spock opted for using his jet boots to expedite the journey. (Star Trek V: The Final Frontier)
Aboard a Galaxy-class starship, the shortest route from the bridge to transporter room 1 on deck 6 included using a turbolift that traveled through turboshaft 4. (TNG: "Brothers") A failure in turboshaft 4 would prevent direct turbolift access from the bridge to main engineering. (TNG: "Remember Me")
Emergency bulkheads were installed in turboshafts and could be initiated to stop a turbolift from falling or to restrict access for unwanted passengers of a turbocar. Turbocars were also equipped with emergency clamps that would act as brakes and anchor the car inside the turboshaft in case of power loss. (TNG: "Power Play", "Disaster")
Jean-Luc Picard was trapped with three young children in an unstable turbolift when the USS Enterprise-D was hit by a series of quantum filaments. His group used a ladder mounted on the turboshaft wall to escape. (TNG: "Disaster")