Capacitor in series

What is meant by equivalent capacitance? The equation of equivalent capacitance in series is 1/C = 1/C1 + 1/C2 +.... However, the charge stored in the equivalent capacitor is equal to that in the individual capacitor (but not equal to the total charge stored in the circuit). So, why does it call the equivalent capacitor?

Equivalent means that you can replace the 2 or 3 etc capacitors in series by one single capacitor that would have exactly the same effect in the circuit.
Imagine the series capacitors inside a black box with just the connections to the two at each end sticking out.
The theory is that if you connect those connections to a supply, you would not be able to tell the difference between there being just one capacitor in the box, with that equivalent value, or the 2 or 3 etc separate capacitors.

So for example, the 2 capacitors in the box here have a charge, shall we say, of 4 Coulomb each, represented by the 4 plus and minus signs.
If you connect to that system, you just see the 4 minus charges on the right capacitor, and the 4 plus charges on the left one. As far as you can tell, you have a single capacitor in there with charge 4 coulomb. You calculate the value of that capacitor, and hence the charge on it when connected to V, with that 1/C = 1/C1 + 1/C2 formula.

Is it because the charge between the two capacitor would be cancelled out each other so that we could not observe any charge between them?