Two plates and a gap
Every capacitor is two conductors separated by an insulator. On the left is the basic idea; on the right is how a real component packs it into a small can.
The plates
Two metal plates face each other closely but never touch. The bigger their area, the more charge they can hold.
The dielectric
Between the plates sits an insulator such as plastic film, ceramic or oxide. The thinner it is and the better it polarises, the higher the capacitance: C = ε·A / d.
Charging
A battery moves electrons off one plate and onto the other. Equal + and − charges build up facing each other, and the energy is stored in the electric field across the dielectric.
Layers to roll
To get a huge plate area, a real capacitor uses long strips: foil, film, foil, film. The second film keeps the foils apart once the stack is wound.
The winding
The strips are rolled into a tight cylinder. Seen from the top, the two foils spiral side by side, always separated by film.
Can and leads
Each foil is joined to a lead, the roll goes into an aluminium can, and a rubber seal closes it. The result is the familiar two-legged component.