Measuring a microhm-range resistance with two leads is hopeless: the resistance of the leads and their contacts — of the same order or larger — adds to the reading and ruins it. The four-wire, or Kelvin, method separates the two functions: two leads inject the current and two separate leads measure the voltage drop directly across the object.
It works because the voltmeter has a very high impedance and practically no current flows through its leads, so their resistance produces no drop and does not enter the result. What is measured is the voltage that genuinely exists between the points where the voltage clamps rest.
It is mandatory for any low-resistance measurement: breaker contacts, busbar joints, transformer windings, shunts and battery connections. In practice the clamp order matters — voltage clamps always inside the current clamps — and on inductive loads the current must be allowed to settle.