Capacitor Applications
Capacitors (including tantalum) are often used in the following applications.
Backup (Battery)

Utilizing as a battery
When the load current increases due to power supply interruption or a sudden rise in IC drive speed, the line voltage from the power supply may drop, possibly causing IC malfunction. To prevent this, charge stored in a capacitor is supplied to the IC, temporarily maintaining the line voltage.
Decoupling

Utilizing AC characteristics
To supply stable DC voltage, capacitors are used to remove high-frequency noise caused by high-speed circuit drive or externally induced noise superimposed on the power supply line. Adopted in general power supply circuits.
Coupling

In this application, the capacitor removes the DC bias voltage from the previous stage and only passes through the AC signal voltage.
Typically adopted in audio circuits.