what do these HVAC levers do?
Those levers control a flap inside the duct.  If the handle is parallel with the duct, it is fully open.  If it is perpendicular to the duct, it's fully closed.  And you can set it anywhere in between to fine tune the flow.

If you have an area that you never use, you can close it off to save on the utility bills.  But don't completely close it because you want some amount of air circulation so it doesn't get musty.  You can also manipulate what is fully open and what is partially open to do more work in selected areas.  As Ed Beal points out, some systems are designed around one part of the house getting more flow than another, like a 60/40 split, and that mix being seasonally adjusted.  

However, the heating and cooling system is designed around exchanging heat with a certain volume of air moving through it.  If you block significant air flow so less total air than intended is moving through the air handler, the system's operation will be less than optimal.  You could even stress the equipment if you block too much.

Sometimes, the system isn't well designed, and a room far from the air handler just doesn't get a lot of air flow.  It can be helpful to add a small vent fan in that room to pull more air.  I've used a little add-on fan like this and it helped a bit: