A conductor is a type of material that allows the flow of an electrical current in one or more directions. In an aircraft wiring harness these conductors are what power the aircraft and carry data back and forth between components. Some examples of materials that are good conductors include silver, gold, copper, and aluminum.
An aircraft like the F-16 or UH-60 can contain thousands of feet of electrical wires, and at the core of each of those wires lies the conductor(s). A wire may be as simple as a single conductor covered by an insulating material, or it may be composed of multiple individual insulated conductors grouped together and surrounded by an overall insulating jacket.
The picture below is an example of a multi-conductor cable that would be typical to find in an InterConnect wiring harness. You can see that the white and blue insulating jackets have been stripped back to expose the conductor material.