What does switching back of amp from 8 to 4 ohms do?

Another situation where lots of brilliance has mixed in with lots of confusion. 
 

Maybe a different approach here is in order, maybe trying to understand the mechanical wiring differences Beyond the four and eight ohm taps. Clearly there are wiring differences within the speaker cabinet relating to four and eight ohms. What are these differences which seem to have operational merit.

@gregdude 

You're right Greg.  Russ's answer is pretty much the same as most of the others.

Very few speakers have traces that don't go below 6 ohms.  Ergo very few speakers should be connected to the 8 ohm tap.  Mainly only 'full-range' horns and that kind of rarely used stuff.

Also consider the phase angle.  Bad combinations of phase angle and low ohms at particular low frequencies mandate the 4 ohm tap.  Read John Atkinson's tests in Stereophile.

@russ69 you said all the above answers are wrong but don't say how, I'm curious if you want to back that up.

All wrong answers so far. Loudspeaker impedance is never one raw number, the word we use is nominal impedance. In most cases you could use the 8 ohm taps or the 4 ohms taps. Most of us try both and use the one we think sounds best. There are exceptions with loudspeakers that have very low impedance points. If you have a loudspeaker that dips well below 4 ohms, you'll pretty much want to use the 4 ohms taps but that question seldom comes up because it's rare to see hard to drive loudspeakers hooked up in a multi-channel system. 

Thank you again
Fascinating response, with the DC resistance of the voice coil being low I would expect lower power needed.  Why is more power needed? 
 

Inside speaker is inductive coil that expands and contracts when voltage is applied to move the driver. The DC resistance of voice coil is extremely low almost to the point of short circuit. Therefore lower frequencies require a lot larger power.

Czarivey, Great answer but the very last sentence confused me.

I was told changing to four ohms, since my speakers explore below eight ohms, is helpful when the lower range is used by the speakers. Not sure how the speaker is wired within the speaker to accommodate four and eight ohm settings. I guess it's a design way for channeling more power to the lower end of frequency range which Impacts sound level. Using McIntosh amplifier with transformer.

Speakers normally never will have stable impedance, but the rule is far simpler. If speaker impedance chart does not go below 8 ohms, then use 8-ohm binding posts. Otherwise use 4-ohm binding posts. 

If you change switch for 8-ohm speakers the following will happen:

If your speakers are 8- ohm you may lose a-bit of the volume, but you'll gain dynamic headroom and clarity. If your speakers are below 8-ohms, you may lose a lot of low-frequency resolution and larger loss of volume.

If you have 8 Ohm speakers, set it to 8 Ohms. If you have 4 Ohm speakers set it to 4 Ohms.

If your speaker Ohm rating isn't on their back look their specs up online.