A milliohmmeter is used to measure very small resistance values. This meter is used to measure electrical bonding of structures, racks, flamesprays, antennas, probes etc.
A standard ohmmeter puts a voltage on a system and measures the current through the circuit to calculate the resistance of the circuit using ohms law.
U=I.R
I=U/R
R=U/I

A megohmmeter puts a high voltage on a circuit to measure high resistances.
If we were to put a relatively high voltage on a circuit that has a very low resistance we would create a large current. (I=U/R, so if we make resistance R very small, the current I will get large).

(A standard ohmmeter connected to a voltmeter to measure the voltage.)

If we take for example a standard ohmmeter with a voltage of 0.6 volts and a resistance of 10 milliohm (0.01 ohm) we have this formula:
I=U/R or I=0.6/0.01 or I=60 amperes. That is a way too high current for a battery to deliver.

Therefore a standard ohmmeter is unable to measure small resistance values. For this purpose we use a milliohmmeter.
The milliohmmeter works by a different principle. This meter doesn't put a voltage on a circuit to measure the current, it puts a current on a citcuit and measures the voltage.
If we are measuring a low resistance circuit and we put a voltage on it, the current goes sky high but if we put a small current on the system, the voltage would be in the millivolt range wich can be measured by a internal voltmeter.
Let's say that we put 10 milliamperes on the same circuit as before wich should be no problem for a battery to deliver.
Now U=I.R or U=0.01x0.01 or U= 0.1 millivolt.

The milliohmmeter uses 4 leads (Kelvin leads) to measure the circuit. This way, the resistance between the current lines and the circuit (cable resistance and transition resistance between clamp and circuit) do not influence the reading as long as they are not large enough to force the meter to reach its maximum voltage to keep the current at its designed level.

The probes wich measure the voltage drop over the resistance still need to have good contact to measure the right value as any resistance in these probes affect the measured voltage drop in the milliohm meter.