Ah yes,
As you turn the arrowed knob in a clock wise direction , the arm at right angels to the knob should swing upwards so its end now sits at the same level as the mantle. The arm stops in the verical position but if the knob is turned further the gear wheel transfers the rotation to a shaft inside the arm, which ihas a knurled end (now at the top) which should grind on a flint helt in the cap at the end of the arm. This should spread a shower of sparks towards the mantle to ignite the gas.
The reason the arm is designed to swing is so it can be moved away from the mantle to stop it over heating once its lit and being damaged. So once its lit, the arrowed nob should be turned anticlockwise to set the arm down in the position in the photograph.
Edit - as anyone who has used mantle lamps will likely know once the mantle has been burned for the first time, they become incredibly fragile, and careless lighting with a match or spill can easily puncture or destroy a mantle. this device allowed the lamp to be lit without removing the glass globe, improving the protection for the mantle.