How does this current monitor circuit works?
Can you please explain how can I analyze and equate its feedback?


It works on the principle of a balanced bridge (although it doesn't like like it). The load current causes a load-dependant voltage at the inverting input and the op-amp tries to match that voltage at the non-inverting input. It does this by turning on/off the FET so: -

+Vin always is trying to match -Vin.

If \$I_{LOAD}\$ is 1 amp then one-thousanth of one-amp is taken through the 100 ohm resistor thus +Vin = -Vin. 

If +Vin is a little too high (compared to -Vin) then the op-amp output rises and turns the FET on more and more current flows thru the 100 ohm so that +Vin lowers and, on a micro-second timescale, the two inputs eventually match.

As for your circuit, try using a JFET model instead of a MOSFET model. The gate drive needed to produce the correct voltage on the output will necessarily be too high in your simulated circuit. You can prove this by trying load currents of say 100mA. With that current you'd expect to see 100uA through the 5k resistor producing a voltage of 0.5 volts - to turn the MOSFET on, the gate would need to be possibly 3 volts higher at +3.5 volts. Clearly, on a 1 amp load the voltage expectation across the 5k will be 5 volts and this won't work because your op-amp supply is only 5 volts.

With a JFET, the device can fully turn on when the gate voltage is maybe a volt below the source voltage.