How does charge work in a capacitor circuit with alternating current.

I understand that electrons go from battery to one side of plate forming a negative charge but then somehow charge flows out from the positive plate through the other side of the battery and towards the negative plate until capacitor = supply voltage.
Does the Di electric or electric field cause flow to push out from the positive side or have I got it wrong.
Would like an explanation without formulas if possible.

when capacitor is connected to circuit with some sources (ac or dc voltage sources), current flow until capacitor charges up. if the voltage source is AC, capacitor keeps on trying to charge up to level of the source (this means it keeps charging/discharging). when capacitor is charged, it's dielectric is polarized. in ac circuit due constant changes (charge/discharge) polarization changes as well. current does not flow through capacitors insulation but there is current flow through capacitor leads.

impedance of capacitor in ac circuit is therefore
Xc = 1/(j*2*pi*f*C)
where
j=sqrt(-1)
pi=3.14
f=frequency (Hz)
C is capacitance (F)

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