In a 4-terminal resistor, an ultra-precise resistor (green) is connected to 4 terminals through small, but unknown, resistors (red). These unknown resistors are the combination of lead resistance, screw terminal resistance, connection wire resistance, and other sources of errors.
Typical values for these unknown resistors range from 0.01 ohms to 0.2 ohms, and the values are often unstable. The values can change when you loosen or tighten a screw, for example, or if you substitute a longer test lead.

To use a 4-terminal resistor, we force a current from Terminal 1 to Terminal 2. It’s current, so the unknown resistances attached to Terminal 1 and Terminal 2 don’t affect the amount of the current. The same number of electrons per second flow through from T1 to T2, regardless of the resistance.

 
A voltmeter measures the resulting voltage drop across the ultra-precise resistor, measuring through the unknown resistors attached to Terminal 3 and Terminal 4. The voltmeter’s input impedance is very, very high compared to the unknown resistors, so the unknown resistors have essentially zero effect (typically less than 0.1 parts-per-million).
 
So the current flows through the 0.1 ohm resistor, unaffected by the unknown resistors, and we measure the voltage across the 0.1 ohm resistor, unaffected by the unknown resistors.
 
And that’s how a 4-terminal resistor works.

 
So what errors do we worry about when we’re using this type of resistor? We typically measure these errors in parts-per-million, or PPM (one PPM = 0.0001%).
 
There are five major sources of errors: calibration uncertainty, inductance, temperature, aging, and metal-to-metal contacts. Resistor manufactures, like Microhm Electronics, are always try best to avoid these errors, especially for the high-end 4-terminal resistors, so as to being a better resistor provider.