I don't want to annoy anyone here by giving 'wrong' non-academic info but impedance can be a toughy to explain.
As mojoman pointed out, it is generally thought of as the resistance of a circuit to AC signals. 'DC resistance' when thinking of resistors, will behave the same with AC and DC signals (in an ideal world). So, say a voltage divider of 1/2 would reduce 10v to 5v. And an AC signal from 0-10v (say a sine wave off set, centre at 5v) to 0-5V.
But when dealing with components like inductors and capacitors, these 'resist' AC signals differently depending on the frequency of said signal, and the components value. using the above voltage divider example, if one replaces one of the resistors with a reactive component (cap, or inductor) then the voltage division is no longer fixed, it becomes dependant on the frequency of the singal. Google 'RC low pass filter' and see what you get.
As I said, I'm not giving you the full story here, just basic practical stuff.
In terms of 'high/low impedance inputs/outputs... in lay terms, a high impedance input will not 'use' the input signal as power...as that could change the signal itself. Puting a high impedance output, to a low impedance input would degrade the signal. In audio it would reduce the high frequency components.
With outputs, a low impedance output has the ability to 'drive' inputs. That is not to say necessarilly that it has a lot of power, but the signal is not too weak for something its put into to affect it. As a rule of thumb with basic audio, outputs should be low impedance, inputs should be high impedance.
A buffer, or 'voltage follower', with a gain of 1 does nothing except prepare a signal for another part of a circuit, or to an output. It 'looks' at a high impedance output from something, and copies it to its output, without using much of that input signal (which would change the signal itself).
So you can see why buffers are used everywhere as they convey information about a signal, without affecting it. All components require 'power' but we don't want to use signal inputs as power (sometimes we do
), we are just interested in the information they contain.
If you have an audio circuit that modifies the signal in some way and its 'active' (ie: powered) its probably a good idea to have a buffer at the input, and one at the output. Neither changes the signal in any way but it allows various impedance sources to be connected to the input and output. Otherwise, the circuit *could* have a different effect depending on what devices you connect to it...Prime example is a guitar amp.
Hope that helps. As I said, its not academic info, my analogue is terrible and ecerfoglio's explaination was spot on. But it sohuld help o clear some things up.
Blueteeth