Definition/Summary
The impedance of a load (a combination of components) in an AC current is a complex number $Z\ =\ R+jX$ where $R$ is the resistance of the load and $X$ is its reactance.
It can also be written in polar form: $Z\ =\ |Z|e^{j\phi}$, or as the phasor $|Z|\angle\phi$.
Impedance is the AC equivalent of resistance: it is used in the AC version of Ohm’s Law: $V_{complex} =\ I_{complex}Z$
(or $(V_{max}/I_{max})\angle\phi =\ Z,\text{ where }\phi$ is the phase difference by which the voltage leads the current), and it obeys the same series or parallel combination laws as resistance does.
Impedance depends on frequency (except for pure resistances).
Impedance is measured in ohms ($\Omega$).
Equations
For a load across which the voltage leads the current by a phase angle $\phi$:
$$Z\ =\ |Z|cos\phi + j|Z|sin\phi\ =\ R+jX$$
(in polar form: $Z\ =\ |Z|e^{j\phi}$)...