When there is a current in a wire, electrons collide with the ions in the lattice of the metal. Some electrical energy is transferred to thermal energy, so the wire gets warm. In a connecting wire this heating is unwanted, because the energy is wasted to the surroundings. We therefore use low resistance wires wherever we can.
There are three main ways to lower the resistance of a wire. Use a short wire, because the electrons collide with fewer ions on the way through. Use a thick wire, because a larger cross-sectional area gives the charge more room to flow. Use a metal that is a good conductor, such as copper.
The heating also depends on the current. A wire carrying a large current needs to be thicker, so a cooker cable is thicker than a lamp cable. This stops the wire getting too hot, which would waste energy and could start a fire.