Let's say, for example, that you have a straight wire, not connected to anything else, and a voltage. The voltage will make electrons move along the wire, and they will move for a very brief time, but electrons will soon build up on one side, and there will be a lack of electrons on the other side. The side that has a surplus of electrons will repel additional electrons, and this force will soon be equal to the force they experience from the voltage source. Similarly on the other side - the lack of electrons will pull electrons back, not allowing more electrons to get out. This "short time" is typically a very small fraction of a second, for example a few microseconds.