That is what is known as an “Octane Selector”. It allows you to adjust timing based on available gasoline quality.
From the days when you could just about run kerosine, and the octane varied depending on where you live. I remember setting these up and then someone sees the distributor move around when you give it some gas, and confuses the hell outa them!
The octane selector is the little tab with the arrow. With the type and characteristics of the gas, you would adjust the timing so it just starts to ping at low speed and full throttle. The other gadget is not stock. Since the vacuum advance rotates the distributor to advance/retard timing as necessary, the gadget with the two nuts is supposed to limit the rotation of the distributor, thus fine tuning the amount of advance. Doesn't seem necessary to me, but it probably worked. Sounds like one of the gizmos that JC Witney would sell.