This article is from the Audio Professional FAQ, by with numerous contributions by Gabe M. Wiener others.
We can talk about the characteristic impedance of an input, which is
to say the ratio of voltage to current that it likes to see, or how
much it loads down a source. (You can think of this as being an "AC
resistance" and you would be mostly right, although it's actually
the absolute magnitude of the vector drawn by the resistive and
reactive load components. Dealing with line level signals, reactive
components are going to be negligible, though).
In general, in this modern world, most equipment has a low impedance
output, going into relatively high impedance input. This wastes some
amount of power, but because electricity is cheap and it's possible to
build low-Z outputs easily today, this is not a big deal.
With microphones, it _is_ a big deal, because the signal levels are
very low, and the drive ability poor. As a result, we try and get
the best efficiency possible from microphones to get the lowest
noise floor. This is often done by using transformers to step up
the voltage or step it down, to go into a higher or lower Z load.
Transformers have some major disadvantages in that they can be
significant sources of nonlinearity, but back in the days of tubes
they were the only solution. Tubes have a very high-Z input, and
building balanced inputs with tubes requires three devices instead
of one. As a result, all mike preamps would have a 600 ohm balanced
input, with a transformer, driving a preamp tube. Today, transistor
circuits can be used for impedance matching, although they are often
more costly and can be noisier in cases.
As a result of the expense, consumer equipment was built with high-Z
microphone inputs, and high-Z microphones. This resulted in more
noise pickup problems, but was cheaper to make. Unfortunately this
still held on into the modern day of the transistor, and a lot of
high-Z consumer gear exists. Guitar pickups are generally high-Z
devices, and require a direct box to reduce the impedance so that
they can go into a standard 600 ohm mike preamp directly.
Many years ago, the techniques that were used in audio came
originally from telephone company practice. Phone systems operate
with 150 or 600 ohm balanced lines, and adoption of this practice
into the audio industry caused those standards to be used. In the
modern age where lines are relatively short and transformers
considered problematic, the tendency has been to have low-Z outputs
for all line level devices, driving high-Z inputs. While this is
not the most efficient system, it is relatively foolproof, and
appears on most consumer equipment. A substantial amount of
professional gear, however, still uses internal balancing
transformers or resistor networks to match to a perfect 600 ohm
[Ed. note: Modern equipment works on principles of voltage transfer
rather than power transfer. Thus a standard audio circuit today is
essentially a glorified voltage divider. You have a very low output
impedance and a very high input impedance such that the most voltage
is dropped across the load. This is not an impedance-matched
circuit in the classic sense of the word. Rather, it is a "bridged"
or "constant voltage" impedance match, and is the paradigm on which
nearly all audio circuits operate nowadays. -Gabe]