The amount of current that flows through a circuit is determined by the number of electrons that are moving and the speed at which they are moving. The more electrons that are moving and the faster they are moving, the greater the current will be.
The potential difference between two points in a circuit also affects the current that flows. The greater the potential difference, the greater the current will be.
The resistance of a circuit also affects the current that flows. The greater the resistance, the smaller the current will be.