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Think of a capacitor as a water tank with a springy divider in it. The wires are like pipes either side of the divider.
Water can flow into the tank in one pipe. Exactly the same amount flows out of the other pipe. The more water that is put in one side, the more the divider is stretched and the more pressure is needed.
Water cannot flow continuously because of the divider. This is like a capacitor blocking DC.
If there is little flow, pressure changes on one side will be seen on the other side. This is like the capacitor passing AC current.
Imagine a capacitor consisting of two parallel conductive plates close together but separated by an insulator. If you apply a positive voltage to one plate it will force more electrons into that plate This generates a negative electric field across the gap to the other plate. The field repels electrons from that plate causing them to flow out. The amount of electrons that flow is proportional to voltage and amount of capacitance (determined by the size of the plates and inversely to their separation distance). And, of course applying a negative voltage will cause electrons to flow in the opposite direction.
For a step change in voltage the flow will continue until the charges on both plates are equalized, then stop. For a continuous change in voltage (AC), the current will continuously flow to equalize the charges.
From this I'll leave it as a exercise for the reader to explain why the impedance of a capacitor goes down with an increase in AC frequency.
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