Acoustic impedance in geophysical context
This concept actually comes from the electrical. They define the impedance as $Z=\frac{V}{I}$. 
Where V is potential difference/ voltage and I is current.

In acoustics, a similar expression can be obtained using the plane wave equation. 
Since,
                $$\partial_t V = -\rho^{-1}\partial_xP$$
where $P$ is pressure and $V$ is velocity.
Now take fourier transform of both sides and defined impedance as $$Z(\omega)= \frac{P(\omega)}{V(\omega)} = \rho c$$
Where, obviously, $P$ is analougous to potential difference and $V$ is analougous to current.

You may refer to any wave theory book for details.