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

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? 
 

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. 

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

@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.

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.