Capacitors in DC circuit

This is one common question which most people consider. It is true that when a capacitor is placed in series with a DC power output it gets charged up and they stop outputing any more current acting like a open switch. But a capacitor is mostly never used like this in a DC circuit. Think of it being used in parallel. One example that I would give you de-coupling or transient suppressor capacitors. 

You can commonly find a capacitor in parallel to the output side of any voltage regulators like LM7805 etc. These capacitors are there as de-coupling capacitor to avoid any output voltage spikes. Say when a 7805 regulating 5V gives out 8V spike due to some reason, this 8V spike should not reach the output as it might damage the 5V sensitive electronics. To prevent this from hapening a capacitor is used in parallel. This parallel cap will provide a low impedance path for the 8V spike voltage to reach the ground rather than get out through the high impedance output, thus filtering the spike voltage before reaching the output.

To know how they are used in amplifiers you have to gid in a bit more deep, but to give an idea they are charged and discharged acting a small power source to contorl a switch like transistor. You can check about the multi vibrator circuits to get an idea about this. 

It is also true that if the device is battery powered (pure DC) you will not need any filtering capacitors in a DC circuit since batteries do not provide voltage spikes.

Used in a direct current or DC circuit, a capacitor charges up to its supply voltage but blocks the flow of current through it because the dielectric of a capacitor is non-conductive and basically an insulator. At this point the capacitor is said to be “fully charged” with electrons.
The capacitor is a component which has the ability or “capacity” to store energy in the form of an electrical charge producing a potential difference across its plates, much like a small rechargeable battery.

There are many different kinds of capacitors available from very small capacitor beads used in resonance circuits to large power factor correction capacitors, but they all do the same thing, they store charge.
Capacitance is the electrical property of a capacitor and is the measure of a capacitors ability to store an electrical charge onto its two plates with the unit of capacitance being the Farad named after the British physicist Michael Faraday.
Capacitance is defined as being that a capacitor has the capacitance of One Farad when a charge of One Coulomb is stored on the plates by a voltage of One volt. Note that capacitance, C is always positive in value and has no negative units.

One thing I need to share additionally, whether the circuit is powered using pure dc or not, it doesn't have any connection with blocking capacitors in audio circuits.

As we all know, audio is a form of AC signal. A blocking capacitor passes the AC blocking the DC. But fortunately or unfortunately, a single rail power supply based ( no negative voltage, specially when it is operated with battery) the negative peak of the sinusoidal wave are needs to be shifted by the DC it self. Because, as the op-amp do not have negative supply, it couldn't amplify the negative peak of the audio signal. In such a case, whenever the signal is shifted the ampifier amplify the signal and provides the output in an off-set manner. The blcoking capacitors are used to rectify the off-set by blocking the dc voltage and gathering the pure audio signal.