Question from a newbie. What is counterbalancing when referring to the rudder and/or elevator and how do you do it?

An aerodynamic counter-balance is a portion of that flight control that "hangs" forward of the hinge line. It acts like a power boost to make the flight control easier to move. Look at a three view of a Fokker D.VII. note that there are portions of the rudder, ailerons and elevator that are on the front side of each hinge line. Those are the aerodynamic counter balances.
A mass counter balance is a weight that is installed in or on a flight control to balance it on the hinge line also to make it easier to move. These will sometimes show up as streamline shaped things on sticks sticking up over the stabilizer from the flight control.
Some aerobatic planes have triangular shaped plates mounted on rods on the ailerons, these are called "spades" and work like power steering in that they move the flight control towards the stop..
HTH YMMV

I think I understand. In this picture it is the brown part on up, correct?

The reason why I am asking is I am building a Sig Somethin' Extra and have seen some posts referencing counterbalancing and I didn't know what it meant. For rc, is there any real advantages to doing this?

You are correct. It helps RC servos the same way it helps human muscles. It makes it easier for the servo to move the flight control.

For maneuverability , acrobats or what have you there isn't any advantage to doing this on an rc plane?