Since this is a physics q and a, a physics explanation is in order.
There are two kinds of current.
Conduction current is a net flow of charges. It is was people usually think of when the word "current" is used
Displacement current is another form of current, first recognized by Maxwell. Displacement current plays an essential role in Maxwell's equations. Displacement current density is proportional to the time derivative of the change of electric flux density.
When electron current flows into one side of a capacitor, the electrons accumulate, as there is no place for them to go. As the electrons accumulate, the electric flux density changes. This causes, or perhaps "is" a displacement current.
On the opposite plate of the capacitor, a similar process occurs, but with opposite electrical polarity.
The displacement current flows from one plate to the other, through the dielectric whenever current flows into or out of the capacitor plates and has the exact same magnitude as the current flowing through the capacitor's terminals.
One might guess that this displacement current has no real effects other than to "conserve" current. However, displacement current creates magnetic fields just as conduction current does.
This answer is perhaps more than one might want to know, but it is part of the story of electricity that is worth telling.