TLDR: EIS allows us to analyze the time dependent processes occurring in a battery without actually cycling the cell. It's also the easiest place in electrochemistry to fool yourself: a gorgeous fit with the wrong circuit isn't insight, it's fan fiction.
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What is impedance?
Impedance (Z) at its simplest is resistance in an alternating current system. Impedance captures how the system delays the current relative to the voltage when that voltage oscillates.
Because of that delay, impedance has two parts:
Real part (resistance): the part that acts like normal resistance, turning energy into heat.
Imaginary part (reactance): the part that comes from energy being stored and handed back instead of lost. This is what creates the timing offset between voltage and current. Capacitors and diffusion show up here.
EIS is powerful because it gives you access to hidden processes inside a working battery. It's dangerous because the data can look more definitive than it really is.
What EIS actually does
Instead of forcing a battery through a full charge or discharge, you apply a very small electrical signal and measure how the cell responds. That signal is usually small enough that the battery stays close to its original state, which is exactly what makes EIS a gentle, non-destructive test.
The useful part: EIS doesn't ask the battery one question. It asks the same question at many different speeds.
High frequencies probe fast processes, often ohmic resistance, contacts, electrolyte resistance, or surface films.
Mid frequencies probe charge transfer and double-layer capacitance.
Low frequencies probe slow mass transport, like lithium diffusion.
That frequency sweep is the whole trick. And because the meaning of any given feature shifts with state of charge and cell age, the same battery can hand you a different-looking spectrum depending on the day you measured it.
Why battery people care
A normal voltage curve might tell you a battery has high polarization. EIS helps you separate where that polarization is coming from.
Is it the electrolyte? The interface? A surface film? A charge-transfer limitation? A transport problem?
EIS does not answer those questions automatically. What it gives you is a way to start pulling overlapping processes apart, which is more than a voltage curve will do for you.