What does a 'capacitor to constant voltage mean?'

[LongApple]

Original context:
"The capacitor acts like an open circuit to a constant voltage"

Does it mean that the voltage across the capacitor is somehow being constant?

Does it mean there an adjacent fixed voltage source?

What is physically happening with the electrons that would make the capacitor act like an open circuit?

If it is easier to explain pretending that there are positive charges traveling instead of electrons, please do so

 

[NascentOxygen]

iginal context:
"The capacitor acts like an open circuit to a constant voltage"

Does it mean that the voltage across the capacitor is somehow being constant?

The current that flows into a capacitor is given as: i(t) = C. dv/dt

When the capacitor's terminal voltage is unchanging, then dv/dt is zero. So current is zero.

When there is a voltage present yet no current is flowing, such an element has the appearance of an open circuit. So, charge has built up on the capacitor plates until its voltage exactly equals that of the circuit it is connected to, and from that time on no more charge can be added to the plates. Zero charge flow equates to zero current in the capacitor.