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An ohmmeter measures resistance by passing a small constant current through the resistor, and then measuring the voltage drop across the resistor. The circuitry is calibrated to read the result in ohms.
The problem with a 2 wire ohmmeter is that the current used to measure the resistance also passes through the resistance of the same test leads that are used to measure the voltage across the resistor. So what you are actually measuring is the resistor in the circuit PLUS the resistance of the test leads.
The 4 wire ohmmeter, or Kelvin connected ohmmeter, uses one set of test leads to supply the constant current, and a separate set of test leads to measure the voltage drop across the resistor. That way the voltage drop across the test leads from the constant current source isn't seen as part of the measured resistance. This allows very accurate resistance measurement of very small resistances.
An explanation with illustrations is available at: