Disposable handwarmers basically purposely cause fine iron filings to rust when activated. This is an exothermic reaction and therefore releases heat.
Reusable packs are similar [(relevant Technology Connections)](https://youtu.be/Oj0plwm_NMs) but use a chemical solution instead. When cooled to the appropriate temperature then activated, they begin to crystallize and this process releases the heat. The video I linked does a good job of explaining this in more detail.
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