I have an older Sony home theater system. When setting the speakers up it asks for me to set the distance of the speaker. Set the distance to what? I have set the distance from the viewing chairs to the speakers, Is this correct or should it be the distance from the speaker to the amp. via the wire footage?

What you did is correct. It's for timing purposes. Sound waves in air. Electrical signals travel may be 80% the speed of light. Sound in air travels much slower.