How Does Understanding How It Works: A Guide Simplify Complex Concepts?

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How exactly does it work?
 
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According to [tex]\nabla \times E = -\partial B / \partial t[/tex], a time-varying magnetic field induces a divergence-free E field; where this intersects a metallic conductor it results in eddy currents and ohmic heating. The magnetic field can be generated by running alternating current through a solenoid.

Then there's a different mechanism that relies on ferromagnet hysteresis loops.

See http://en.wikipedia.org/wiki/Induction_cooker#Technical_aspects