Aluminium capacitors function on the same principles as any other types of capacitors. They are passive electronic components that are capable of storing energy. Capacitors store energy in an electrostatic field.
The capacitor functions when there is a potential difference created across the conductors in the capacitor. The insulating parts of the capacitor develop an electric field. This separates the charges. The positive charges will collect on one of the foil plates in the capacitor and the negative charges will collect on the other foil plate in the capacitor.
This allows the capacitor to function as a type of battery. Once they reach their rated voltage, they stay at that voltage, as well, giving them other useful applications.
While capacitors are very valuable and very common electrical components, none of them are ideal. In an ideal capacitor, the amount of energy stored would be constant. No capacitor is ideal, however, so leakage and other factors always have to be factored into choosing a capacitor for a given application.
The design of the capacitor will depend upon the capacitance that it actually offers. In capacitors that have a very small capacitance, metal coatings over ceramic discs oftentimes provide the conducting surfaces and wire leads are attached to the coating, providing a means of integrating the device into a circuit.
If you were to disassemble a large capacitor, such as the type found in the back of older televisions, you would find a stack of plates and discs. In some larger capacitors, you would also find a layer of metal film on the surface of an insulating film. Paper and plastic are oftentimes utilized in these designs.
In very large capacitors, the plates and insulators are sometimes rolled up to save on space. This results in the aluminum can type capacitors that are very common in applications with high voltages. These capacitors, of course, do have a very high voltage within them and, because of that, they should never be removed from any electronic device without the proper training and proper equipment required to ensure safety.