Basic question on capacitor usage
I don't understand how a component that blocks current once it is
  charged could be useful.


To be precise, the current through a capacitor is zero ('blocked') if the voltage across the capacitor is constant.

It turns out that this is enormously useful for, e.g., coupling AC signals between circuit functional sections without disturbing the DC operating point.

For example, it may be that the output of an amplifier is a constant 5V plus some time varying (AC) component.

The output is to be connected to, e.g., a speaker that cannot tolerate a constant 5V across (as it would 'burn out').

If an appropriately sized capacitor is connected in series between the amplifier output and speaker, there will be no current through the capacitor and speaker due to the constant 5V at the amplifier output.



However, the time varying component will cause a time varying current through the speaker and, thus, some type of sound will be produced.

Such a capacitor application is called capacitive coupling.

Sometimes, the opposite is required and this called capacitive decoupling. 

Rather than connect a capacitor in series, a capacitor is connected in parallel with, e.g., a power supply.  In this case, the time varying components are undesired and are shunted by the capacitor 'around' the load.

A related and overlapping application is capacitive bypass.



There is much more to be said about capacitor applications which are manifold as a perusal of the Wikipedia article "Capacitor" will reveal.