Connecting wires have a very small resistance, but it is never zero. When there is a current in a wire, electrons collide with the ions of the metal lattice and the wire warms up. In a connecting wire this is unwanted energy transfer, because the thermal energy is dissipated to the surroundings and is wasted.
The resistance of a wire depends on its material, its length and its thickness. To waste less energy we make the resistance as low as we can. We use a material that is a very good conductor, such as copper. We use a thicker wire, because a larger cross-sectional area gives the electrons more room to flow and lowers the resistance. A longer wire has a higher resistance than a short one, so we keep the wire as short as the job allows.
Reducing the current also reduces the heating, because less charge passes each second. There is always a compromise: thick copper wire costs more and is heavier than thin wire.