The thickness of wires, at least in the United States, is usually communicated in terms of its AWG size, not its circumference or diameter.
AWG, or American wire gauge, is a wire sizing system which is generally used for round, solid-core wiring that is designed to conduct electricity. The system is used in coordination with the ASTM standard B 258.
The gauge sizes are inverse, so a higher gauge number means a smaller diameter wire. That is so that that a 10 gauge wire would be considerably thicker than a 30 gauge wire.
Thicker wires are stronger (more resistant to physical damage) and are able to conduct higher amperage levels.