The underlying differential equation for this very minimal model is a non-dimensional version of the equation for an RC circuit, with charge measured in units of C*emf, and time measured in units of RC.
The [charge] of the capacitor is a stock.
The [current] flows into the capacitor increasing the [charge].
The [current] depends on the instantaneous [charge] of the capacitor: The greater the [charge] already deposited in the capacitor, the smaller the [current]. Specifically, the [current] is equal to 1 - [charge].
As a result, the [charge] grows exponentially to its maximum value of 1, while the [current] decreases exponentially to zero.