Cara wasn't too far off with her explanation of impedance, but as an electrical engineer, I found it incomplete. I don't think Ohm's Law was mentioned. Ohm's Law states that a pure resistance will have a voltage across it (i.e., between two terminals), at any instant, that is proportional to the current through it at the same instant. This is true of both DC and AC. Resistors dissipate electrical energy (convert it to heat).
Of course, in the real world, we do not deal with pure resistances. We have capacitance and inductance, which store energy rather than dissipate it, and can return the stored energy to their environment under the right conditions. If capacitance or inductance are present, then instantaneous voltage is proportional to the rate of change of current (for inductance), or the instantaneous current is proportional to the rate of change of voltage (for capacitance). If the voltage or current applied to the inductor or capacitor has a sinusoidal waveform, then voltage will either lead or lag current by 90 degrees (lead in the case of inductors, lag in the case of capacitors). Think sine and cosine functions, which look identical except for the 90 degree shift (sine of 90 degrees is equal to the cosine of 0 degrees, sine of 180 degrees is equal to the cosine of 90 degrees, and so on). The peak amplitudes of AC voltage and current will be related by a ratio that is analogous to resistance, and which is called reactance. Reactance differs from resistance in that the values being compared are out of phase with each other. This out-of-phaseness is the reason ideal capacitors and inductors don't dissipate energy; they store it for part of a cycle and give it back during the rest of the cycle.
However, just as there are no pure resistances, there are no pure capacitances or inductances in the real world (ignoring superconductors). Components have a combination of resistance and reactance. AC voltage and current waveforms are not perfectly in phase, but they are not 90 degrees out of phase either. They are somewhere in between. So the component will dissipate some of the energy that is input to it, store the rest, and later give back the stored energy as it moves through an alternating current cycle.
Impedance is the combination of resistance and reactance. For reasons related to Euler's identity, in circuit analysis, reactances are expressed as imaginary quantities, while resistances are real quantities; therefore, impedances have values expressed as complex quantities (a complex number is the sum of a real number and an imaginary number).
Ohm's Law can be rewritten using impedance in the place of resistance, and a complex-valued representation of the voltage and current. The result is a more generalized version of the law, which is applicable to AC circuits.https://en.wikipedia.org/wiki/Electrical_reactancehttps://en.wikipedia.org/wiki/Electrical_impedancehttps://en.wikipedia.org/wiki/Euler%27s_formulahttps://en.wikipedia.org/wiki/Ohm's_law