What is this springy thingy in the back of my Rochester 4brl, and what does it do????????

 

That's the hot idle compensator.

Under the cover is a bimetallic strip with a rubber end, which closes an air bleed hole that goes into the manifold.
When the engine gets hot (such as idling in traffic on a hot day) the strip deflects, opening the hole, and allowing in extra air to lean out the mixture to prevent an over-rich condition.

The spring there is a button you can use to hold the valve closed when tuning a hot engine, so as to make your settings accurate.

See your '68 Chassis Service Manual.

- Eric