The circuit is a true function circuit without hysteresis, something impossible to attain with a comparator. The circuit is redrawn below for explanatory purposes. The block labeled "feedback" is a well-known configuration that outputs the larger of the two IN(+) input voltages on U2 and U3, or Vf=MAX(Vout,2V) in the notation shown. Among other things, this means that Vf= IN(-) node of U1 is always >=2V, so that for Vin2V, U1 will drive its output towards the positive rail in the amount necessary to force its IN(+)-IN(-)=0, or Vf=Vin. This means the circuit produces Vin=Vf=MAX(Vout,2V)=Vout for Vin>2V. The circuit will amplify the ever present noise for Vin exactly=2V , and if this is a problem then a small amount of resistive feedback from Vout to U1 IN(+) will remove the output noise response.
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. . . feedback . ------------------------- . | | . | .---------------. | . | | | | . | | U3/| | | . | | /-|--' | . | +---|