In a chemical reaction, molecules (themselves composed of a set of atoms) are rearranged in new molecules by creating and/or removing bound between atoms. Creating/removing these bounds will either release or absorb some amount of energy. When the reaction release energy, it is an exothermic reaction. When it absorb energy it is an endothermic reaction. Fire is the energy released by some exothermic reactions, in the form of heat and light.
In one sentence: heat is the measurement of movement of particles, and fire is when particles move very quickly, therefore hot. This is a very very basic explanation of it
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