The coherence length is just the coherence time multiplied by the
propagation speed.
To understand the coherence time,
say you have a wave described, in complex notation, by
$$
E(t) = A(t) e^{i \omega t}
$$
where $A(t)$ is a slowly varying complex amplitude.
You make this wave interfere with a delayed version of itself
and collect the intensity
$$
|E(t) + E(t-\tau)|^2 = |E(t)|^2 + |E(t-\tau)|^2
+ 2\Re\big(E(t)E^*(t-\tau)\big).
$$
where $\Re$ means real part and $^*$ means complex conjugate.
The interference term is
$$
2\Re\big(E(t)E^*(t-\tau)\big) =
2\Re\big(A(t)A^*(t-\tau)e^{i \omega \tau}\big)
$$
If $A(t)$ is constant, or roughly constant within a time interval
$\tau$, then this becomes
$$
2|A(t)|^2 \cos(\omega \tau)
$$
which is the interference pattern.
On the other hand, if $A(t)$ fluctuates sufficiently fast, and $\tau$
is larger than its correlation time, then $A(t)A^*(t-\tau)$ averages to
zero and there is no interference.
Thus, the coherence time can be simply seen as the correlation time of
the complex amplitude $A(t)$.
Now, I'm not sure there is a very quantitative definition of the
correlation time. You could define it as the delay where the
autocorrelation function drops below some arbitrary threshold.
This is equivalent to setting a threshold on the visibility of the
interference pattern.
The relationship with the shape of the spectral line should also be
apparent: the squared modulus of the Fourier transform of $A(t)$ is the
shape of the line (the spectrum of the wave shifted by $-\omega$).
It is also the Fourier transform of the autocorrelation function of
$A(t)$. Thus, when the line is wide, the autocorrelation function is
narrow,and the coherence time is short.
