What is a layman explanation for why the wavelength of light increases when space itself expands? I understand that the universe is generally agreed to be expanding based on observations. What I have read is that space itself is expanding. My question is why does this expansion of space affect the spectra of light itself? 
It has been observed countless time since Hubble that light from distant galaxies arrive to us with spectra shifted to longer wavelengths (red-shifted). If a wavelength of light is defined with a metric of spatial distance, then what is the significance of spatial distance itself increasing? Would not the expansion of space where our instruments of observing light also matter?
To add to my confusion on red-shifts, here is the Planck-Einstein relation: 
$\lambda = \frac{hc}{E_{photon}}$
Wavelength is a function of $c$, but would this constant (distance over time metric) be affected if space dilates? The same rationale goes for time, but I have heard that time at a fixed location would not be affected by the expansion of space, but I am uncertain how time for moving objects are affected. 
 A: here is a layman's explanation:
There is a toy called a Slinky which is a loosely-wound coil spring made of either plastic or flat wire- if you haven't seen one, search on it to get the idea of how it looks. 
We imagine the Slinky resting horizontally on a smooth floor, with its ends pulled apart to some convenient distance so adjacent coils of the spring are spread out and not touching. If you were to lie down on the floor next to it and view it from the side, the wire coils would trace out a sine wave curve. 
Now we pull the ends of the Slinky farther apart, as if the space in which it is embedded were "expanding". We notice that the spacing between adjacent coils of the wire has increased, and in our sideways view of the coils, the sinusoid shape of the spring has "shifted" to correspond to a lower frequency.  
This is analogous to the situation in an expanding space in which high-frequency sine waves are embedded: as space stretches out, so do the sine waves, and their frequency shifts down. 
A: The layman explanation of the expanding universe is a balloon.
But now you have to imagine that observers behave like points on the balloon that do not grow like the waves on the balloon do.


More technically, it should be noted that not only doesn't the experimenter that is measuring the red shift remain unaffected by expansion of the universe but also the metric remains the same (ie the metric/space doesn't expand). 
The Robertson Walker metric $d s^2 =  dt^2 - a(t)^2 \left[ \frac{dr^2}{1-k r^2}+r^2d\Omega^2\right]$ is a solution for an idealized homogeneous isotropic universe, but the universe is coarse instead, and that (expanding) metric should be more like interpreted as the average of the metric. This averaging is done on very large time scales, for instance: even for clusters of galaxies we do not observe that they have expanded in time.
So the reason for the redshift is not the metric expanding (because it doesn't expand) but much more the relative speed of the observer as lurscher indicates in his answer. And an intuitive idea of the redshift/doppler effect is as mmeent explains in his answer: the increasing time delay between two separate moments or peaks of a wave.
A: Here is simple explanation:


*

*Suppose a light source and a observer are in an expanding space. 

*Now think of two subsequent crests of wave emitted by the lightsource.

*The second crest is emitted slightly later than the first one, hence the space has expanded slightly in the meantime. 

*Consequently, the second crest has to travel further to reach the observer, taking more time.*

*Hence, the time between the arrivals of the crests at the  observer is longer than the time between their emission at the source.

*This is the same thing as saying that frequency of the wave is lower, or (since the speed of light is the same) that the wavelength is longer.


*(And since it is taking longer, space expands more while its travelling increasing its travel time a bit more.)
A: The red-shift does not come from direct intervention from metric expansion itself, but from regular Doppler shift, albeit due to the separating velocity between source and detector, which depends itself on the distance between source and detector through Hubble's law
Just for completeness, I'll mention that the original hypothesis that red-shift came from metric expansion itself was historically called the tired light hypothesis, but they are nowadays considered widely disproved by observations
