In more detail
AWG sizes form a geometric series: each step down in number makes the diameter about 12.3% larger, so every 6 gauges roughly doubles the diameter and every 3 gauges roughly doubles the cross-sectional area. 12 AWG is 0.0808 in (2.053 mm) across, 6,530 circular mils or 3.31 mm². Past 1 AWG the scale continues as 1/0, 2/0, 3/0 and 4/0, and thicker cables are sized in kcmil. Thicker wire has lower resistance, so it loses less voltage and runs cooler at the same current.
Why it matters
Undersized wire overheats. In typical North American residential copper wiring, 14 AWG goes on 15 A circuits, 12 AWG on 20 A and 10 AWG on 30 A, but the electrical code and a qualified electrician decide what an installation actually needs. Long runs must also be checked for voltage drop; a common design guideline keeps it under about 3%. Elsewhere wire is sold by cross-section, so a 2.5 mm² cable sits just under 13 AWG (2.62 mm²).
Example
Copper 12 AWG has about 1.588 Ω per 1,000 ft at 20 °C. A 15 A load 100 ft from the panel means 200 ft of conductor out and back:
R = 200 / 1000 × 1.588 Ω = 0.318 Ω
V_drop = 15 A × 0.318 Ω = 4.76 V (3.97 % of 120 V)
The same run in 14 AWG (2.525 Ω per 1,000 ft) drops 7.58 V, or 6.31%.