Why is capacitor used? I don't quite get the practical use of a capacitor. The theory is fine, but in simple words please explain how, why and where capacitors are used? Is there any other equivalent circuit for capacitors? From what I have learnt capacitors are used to store charge, but how does that make it useful in electric appliances?
 A: Capacitors, as used in electric circuits, do not store electric charge.  When we say a capacitor is charged, we mean energy is stored in the capacitor and, in fact, energy storage is one application of capacitors.
Now, for an ideal capacitor in a circuit context, the current through is proportional to the rate of change of the voltage across:
$$i_C = C \frac{dv_C}{dt}$$
where $C$ is the capacitance of the capacitor.
Note that when the voltage across the capacitor is constant, the current through the capacitor is zero.
This property means that a series capacitor can be used to couple signals between two circuit nodes with different DC voltages.
This same property also means that a parallel capacitor can be used to decouple signals between two circuits that share a common DC voltage.
One of the simplest circuits with a capacitor is the RC circuit which has numerous uses.
When combined with a resistor and inductor, we have an RLC circuit which also has numerous uses.
The fact is that the uses of capacitors are so numerous that there is no simple answer.  You can find much more here:  Applications of Capacitors
A: There are two main uses for capacitors.
First, the discharge of a capacitor can provide a very large, brief current. You can charge a capacitor slowly using a low-current source, such as a battery. Then you throw a switch and connect the capacitor across a low-impedance load, a near short.  All of the charge leaves the capacitor in a time of roughly $\tau = RC$, which can be quite brief.  This is how very bright camera flashes work. At the other end of the spectrum, a capacitor between a power supply's "hot" and "ground" terminals will stabilize the voltage provided by the supply, since any fluctuation in the current drawn by the circuit can come from the charge on the capacitor.
The other, more important use, is as a "resistor" whose value depends on frequency. A capacitor transmits fast signals, but blocks slow signals. You can use this to build high- and low-pass filters if you only want AC or DC signals. (The power-supply capacitor I mentioned above is an example of a low-pass filter.) You can also combine capacitors and inductors to make resonant oscillating circuits.
A: Think if a capacitor as a very small but very fast battery...
And in digitals etc. every time something has to be stored a huge number of capacitors is used.
A: As @Benedikt already told, you can use them as fast battery. Furthermore, you can use them in a resonant circuit, or for powering small circuits without the need of an akkumulator. You can use them in high-pass- and low-pass-filters, too, for filtering out high or low frequencies.
