When voltage is first applied across a capacitor, current flows, as electrons move into the capacitor. Depending on the size of the capacitor, this will continue for a period, and then tail off, as the capacitor fills up.
Unlike resistors, capacitors show infinite impedance to direct current; to alternating current, their response depends on the frequency - high frequency signals can pass through a capacitor, but not low frequency. The larger the capacitor, the lower the frequencies which can pass through it.
Capacitors are usually formed by having two conducting surfaces separated by a layer of insulation; the larger the surface, the larger the ability to store electrons (i.e. the capacitance).
Over time, techniques have been developed to pack large surfaces into small volumes. One of the most common is the electrolytic capacitor, which separates two long, narrow layers of metal foil with an electrolye; the foil pair is then rolled up into a cylinder.