From the definition: If there is a charge Q on the capacitor (capacitance is C) plate,
the voltage between the capacitor is Vc=Q/C;
So Vc is the voltage diffenence between capacitor plates.
If there is no charge on the capacitor, then the voltage difference is 0.
If the voltage source Vo is connected directed to one side of the capacitor, and the other side of the capacitor is connected to a resistor R and back to another end of the voltage source.
The voltage on both side of the capacitor are all Vo (the difference is 0).
And the voltage across the resistor is also Vo.
This will cause the current I(t=0)=Vo/R to flow, which in turn will charge the capacitor.
After a very small time interval dt, the charge on the capacitor will be Qc(dt)=(Vo/R)*dt.
And the voltage difference between capacitor will be Qc(dt)/C=Vo*dt/(R*C).
Then the voltage between the resistor will be I(dt)=(Vo- Vo*dt/(R*C))/R
So the current will become smaller when more charge are being accumulated between capacitor plates.