In order to connect an alternating signal into the transistor amplifier in a way that the circuitry that generates the signal doesn't interfere with the operation of the amplifier, and also that the biasing and operation of the transistor amplifier doesn't change the way the circuitry of the source signal operates, we need a way to isolate them from each other.
Since the only component of interest that needs to be shared by both circuits is the alternating signal (AC signal), we need to use a component that will let the ac component pass while blocking the any DC of the bias circuitry or the signal generator.
As you learned in a previous lesson, a capacitor is a component that can store energy in the form of an electric field created by lumping charges close to each other but still isolated. Current cannot directly cross the insulating layer inside the capacitor, effectively blocking any direct current flow.
But something interesting happens when a capacitor is affected by an alternating current. On the positive half of an AC wave, one side of the capacitor is filled with an inrush of electrons, while on the other side, electrons are pushed out to be replaced with holes, until the capacitor is fully charged and no more charges move.
For the moment when the capacitor is charging, the amount of electrons entering one plate of the capacitor is the same as the electrons being pushed out from the other side, almost as if the electrons had just crossed the insulating layer.
When the polarity is reversed the effect happens once again, the electrons are now drawn towards the voltage source, leaving holes in the plate of the capacitor. These holes draw the electrons that were previously pushed away, into the plate of the capacitor. The net effect is again as if the electrons crossed the insulating layer to get to the voltage source.
In practice, it is not the actual crossing of the electrons that is of use, but the movement of them on both sides of the capacitor that can be used as a current in the circuit.
Summarizing, the capacitor blocks any current that tries to directly cross the insulating layer, but it can't stop the electrons from being drawn to or away from the plates, effectively letting alternating voltages get through.
This effect is used to isolate the DC component from both sides while allowing the ac to flow, and is called capacitive coupling.
