Consider for a moment, a cell that is not connected to a circuit, i.e., there is no path for current external to the cell.
The chemical reactions inside the cell remove electrons from the cathode and add electrons to the anode.
Thus, as the chemical reactions proceed, an electric field builds between the anode and cathode due to the differing charge densities.
It turns out that this electric field acts to reduce the rate of the chemical reactions within the cell.
At some point, the electric field is strong enough to effectively stop the chemical reactions within the cell.
The voltage across the terminals of the cell, due to this electric field, is then constant and this is the open-circuit voltage of the cell.
If an external circuit is connected to the cell, electrons flow from the anode through the external circuit and into the cathode, reducing the difference in charge densities which in turn reduces the electric field just enough such that the chemical reactions can once again take place to maintain the electric current through the circuit.
The larger the external current, the greater the required rate of chemical reactions and thus, the lower the voltage across the terminals.
As long as the circuit current is significantly less than the maximum current the chemicals reactions can sustain, the voltage across the battery terminals will be close to the open circuit voltage.
As the external current approaches the maximum current, the voltage across the terminals rapidly falls and when the voltage is zero, the cell is supplying maximum current. This current is called the short-circuit current.