In layman terms:
A high impedance input will distort the input signal less than a low impedance input. THis is due to the signal source having to drive the input as if it were a load- a heavier load is of a lower resistance/impedance which means it will draw more current.
A low output impedance means that it can output into a device with a crappier (aka lower) input impedance and have the signal be distorted less.
In technical terms:
Look at this diagram:
File:Source and load circuit Z.png - Wikipedia, the free encyclopedia
-Every signal source is like a voltage source (vs) that outputs the actual signal. Ideally, this is all a signal source would be, but in real life there is some resistance (Zs) in series with the input of the signal source. So a real signal source is more like a voltage source with a series resistor. The actual signal you are trying to transmit comes from the voltage source, but it must pass through the source impedance (Zs) first, and when it does, it will become distorted by a certain amount. How much it becomes distorted depends on how big Zs and Z_L are relative to each other since Zs and Z_L form resistive dividers.
-A signal input can be thought of as a simple resistor (Z_L) with one end tied to ground, and the other end is the input. The voltage, V_L, that appears across this resistor is the signal seen by the input.
Notice that Zs and Z_L are make a voltage divider. Can you see that as Zs gets larger relative to Z_L, the voltage divider steps down the input voltage/signal VL more and more? THis is not a good thing since the input signal VL just keeps getting more and more different from the actual output signal Vs. IN a perfect world, Zs would be equal to zero so whatever the output signal Vs would be exactly equal to the input signal V_L. In real life we can approximate this by making Zs very small and Z_L very large.
Resistances are used for simplicity in this example. The actual term is input IMPEDANCE, not resistance. THis is because there are also capacitors and inductors in parallel with the resistors forming capacitive and inductive dividers. So in real life, the signal does't just get "stepped-down". The capacitors and inductors behave differently for different frequencies in the signal and the signal becomes even more distorted.