The circuit on top uses a gyrator to simulate an inductor. Inductors can be bulky, heavy, and expensive, so it is often valuable to replace them with cheaper components. The circuit being simulated is on the bottom.
The capacitor passes high frequencies (and sudden changes), causing the + input of the op-amp to be closer to the input signal. (Because of the large (20k) resistor, there isn't much current through the capacitor, though.) The op-amp keeps the – input at the same level as +, causing less current to pass through the 1k resistor, because the voltage is nearly the same as the input. The circuit blocks high frequencies, like an inductor.
The capacitor blocks low frequencies (and steady voltages), causing the + input of the op-amp to be closer to ground. The op-amp keeps the – input at the same level as +, causing more current to pass through the 1k resistor to ground; it passes low frequencies, like an inductor.
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