Every wire has resistance, and resistance costs voltage. In a 12 V system a wire that is too thin acts like a small resistor in series with your load. This means that some of the supply voltage is "spent" heating the wire instead of running the device. This can cause dimmer lights, sluggish motors, or a fire hazard.
American Wire Gauge (AWG) is a standardized sizing system used throughout North America for copper conductors. Counter-intuitively, a lower AWG number means a thicker wire with lower resistance. AWG 4/0 (pronounced "four-ought") is the largest listed here at 107 mm², while AWG 16 is the smallest at 1.31 mm².
The most widely cited rule for 12 V DC wiring (recommended by the ABYC (American Boat and Yacht Council) and common in automotive and RV practice) is to limit the total round-trip voltage drop to 3 % of nominal supply voltage, or roughly 0.36 V on a 12 V system. Beyond 3 % many devices begin to under-perform; at 10 % or more you risk equipment damage and serious heat buildup in the wire.
The physics behind the table below come directly from Ohm's Law. For a round-trip conductor of length L (one-way, in feet), cross-section A mm², and copper resistivity ρ = 0.01724 Ω·mm²/m:
Vdrop = I × 2 × ρ × (L × 0.3048) / A
Setting Vdrop ≤ 0.36 V and solving for the minimum cross-sectional area:
Amin = I × L / 34.27 (mm², with L in one-way feet)
The factor 34.27 comes from 0.36 / (2 × 0.01724 × 0.3048). Once Amin is known, the table below selects the smallest AWG gauge whose conductor area meets or exceeds that minimum.