How does voltage output of a solar cell increase/decrease?
It helps to understand that a solar cell is just an ordinary silicon diode (but awfully wide). It has the same curve. 

As it generates current, the voltage rises. As the voltage rises, the diode starts to conduct (above 0.4V), and shorts itself out. This limits the voltage.

More sun = more current, and you move further up the diode (forward voltage) curve.

"Ah ha" I hear you say, "but how come this is happening at less than 0.5V, not 0.7V?"

Well its a very big diode, so the current per mm is actually quite low, and so its not very far up the curve. Use the simulator to play with the circuit. See that the current is 1 millionth of what a solar cell makes







simulate this circuit &ndash; Schematic created using CircuitLab



The current generated internally is directly proportional to light, and constant at a given light level , 1 photon ~=1 electron. 

If I=1A and your load is 0.2ohms V=E*I gives 0.2V across the cell (and 0.2W power). 

If Rload=1ohm, V=1V, But, the diode conducts at 0.5V. So 0.5A goes through Rload, and therefore 0.5A is going internally through the diode junction (and being lost), and only half the power gets out (0.5Ax0.5V=0.25W).

If RLoad was 0.4ohm, V=0.4V, and all the power (0.4W) gets to the load

So Rload has to change as the light/current changes to maximise the power transfer. Too high, you lose power, too low you lose power.

This leads to the MPPT or Maximum Power Point Tracking controller.