I think I understand. There are two complete wires entering the box. Each contains an insulated black, an insulated white and a bare. The two black ones go across the switch, so one is hot from source, the other is hot to load. The two white are wire-nutted together so they are neutral, and the two bare are wire-nutted together with the ground from the switch body, so they are ground. Have I got it?
The reason I'm asking is because I think the dimmer switch I've ordered will require a neutral connection, unlike the switch I'm replacing. I'm replacing the existing dimmer switch because it's incandescent-only, and I just replaced the incandescent chandelier with a 12V halogen one. A lot of the low-voltage compatible dimmers seem to require a neutral connection. Until the new switch gets here, we're using the existing switch all-on or all-off.