Short answers, pulled from the story.
Electrical impedance is the opposition to alternating current presented by the combined effect of resistance and reactance in a circuit. Unlike resistance, which has only magnitude, impedance possesses both magnitude and phase, making it a complex quantity measured in ohms.
Oliver Heaviside coined the term "impedance" in July 1886. He recognised that the "resistance operator" in his operational calculus was a complex number, and in 1887 he showed there was an AC equivalent to Ohm's law.
Steinmetz generalised Arthur Kennelly's 1893 work to all AC circuits later that same year. He represented not only impedances but also voltages and currents as complex numbers, which allowed him to express AC equivalents of Ohm's law and Kirchhoff's laws. His work was highly influential in spreading the technique among engineers.
Capacitive reactance is inversely proportional to signal frequency, meaning a capacitor opposes low-frequency signals more and allows high-frequency signals more easily. Inductive reactance is proportional to frequency, so an inductor presents increasing opposition as frequency rises. In a capacitor the current leads the voltage by 90 degrees; in an inductor the current lags.
Impedance measurement requires determining the magnitude of voltage and current and the phase difference between them. Common methods include bridge techniques similar to the Wheatstone bridge, LCR meters that measure inductance, capacitance, and resistance directly, and impulse response methods combined with the fast Fourier transform for rapid frequency-wide characterisation.
The reciprocal of impedance is called admittance. Its SI unit is the siemens. Instruments designed to measure electrical impedance directly are called impedance analyzers.