Easiest to understand as a water analogy. Pretend you have a hose, with water flowing through it. The water pressure is the equivalent of voltage (basically how hard it's "pushing"), while the flow-rate is the equivalent of current (the volume of flow). Now suppose some wise guy is playing around, and periodically pinching the hose, interrupting the flow. If you're trying to use the hose, you'll see the flow interrupted every time he puts this thumb over the end of the hose, and you'll see flow, no flow, flow, no flow. Now suppose you instead run the hose into a big tank, and take your water from a faucet at the bottom of that tank. Now when the bozo pinches the hose, your flow probably won't be interrupted, because there will be enough water in the tank to provide some flow, as long as the hose is not pinched for too long. So, the tank "filters" the water, preventing you from seeing short interruptions in the supply. That is precisely what a capacitor does - it stores charge, not water, but filters in precisely the same way as that tank. If there is a disturbance (noise) on the input signal, the output signal will be maintained by the charge in the capacitor for a short period of time. Only longer, or very frequent, noise will get through.
Regards,
Ray L.