Why does shading a single PV panel in a series string reduce the current output of the whole string?
The following is simplified but gives a reasonable idea of what happens.


A PV (photovoltaic) cell acts as a light controlled current source. 
Current is approximately proportional to light level across a wide range of insolation (light level).
The voltage of a PV cell is relatively constant with insolation. 
For silicon cells typically this is in the 0.5V - 0.6V range at maximum power output for a wide range of insolation levels.
A current source will produce its rated current with a wide range of applied voltages.
(Just as a voltage source such as a 12V car battery produces ABOUT the same voltage across a wide range of currents).
You can always cause a cell to conduct LESS than its rated current by not providing a load of low enough resistance to allow that current to flow. BUT for a true current source you cannot cause MORE current to flow by applying a heavier load OR by applying extra voltage across the cell.
SO If you place a  number of current sources / PV cells in series they will each try to produce their rated current at that insolation level. If one cell produces less current than the others (either because it is defective, or lower rated or has less insolation) then it cannot be forced to produce more current. So whatever the lowest current cell produces becomes the current that flows through the series string.




Practical result of shading:

The small shadow on the panel from the 'chimney' reduces the panel output by a measured 30% !!!

Photo by David Pophal. 

30% reduction from shading !!!



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Bypass diodes:

One method of reducing the effect of partial shading of a panel is to place diodes either across a number of substrings or even across each cell.
When a cell is shaded the voltage across that cell rises as the voltage from the other cells is presented as an increased potential across the cell "attempting to drive extra current through it". When a bypass diode is placed across the cell the increased voltage causes the diode to conduct and the current from the other unshaded cells flows through the diode.  Overall panel output may be only minimally affected. 

In some panels a limited number of diodes may be placed across substrings eg 4 x 9 cell substrings in a 36 cell, "12 Volt" panel. This causes the whole substring to be bypassed if any cell in it is shaded. This is of limited value as the reduction in panel output by (in this case) 25% is liable to seriously impact its energy output. Where panels are in a larger series string with an MPPT controller this may still be useful - panel output will here drop by about 25%.
But if several identical panels are in parallel with single isolation diodes per panel, then shading a single cell in a panel will tend to take that panel out of service even with say 4 substrings with their own diodes, as the 25% voltage drop will not allow the panel to contribute. 

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Water analogy:

Imagine that you have a constant displacement pump that transfers a set amount of water from inlet to outlet on each stroke. The amount can be varied by an independent control - it may be 0.1 gallon per stroke or  0.5 gallon per stroke or 1 gallon per stroke or ... whatever.  

Imagine placing say 10 of these pumps in series so that each draws water from the previous one and transfers it to a sealed reservoir at the inlet to the next pump. (eg visualise them pumping water up a hillside) 

Each pump may produce a relatively fixed "head" or pressure from input to output regardless of flow setting. Say each pump produces 1 psi (~= 7 kPa) pressure.

Set all 10 pumps to 1 gallon flow per stroke.
10 pumps in series will produce 1 gallon flow and a pressure of 10 x 1 psi = 10 psi.

Now set one only pump to 0.5 gallon flow per stroke.
With 10 pumps in series the flow rate will be set by the 0.5 gallon /stroke pump./
All 10 pumps will produce a 0.5 gallon /stroke flow rate - probably still at about 10 psi.

The analogy is not perfect but gives a good picture of what happens.

The PV cells are equivalent to the individual pumps, where the flow able to be transferred by a cell cannot exceed the flow coming from the prior cell. 



Note: This started off in litres and psi.
I considered converting to litres and kPa but decided on balance that gallons and psi would be familiar to a wider audience.