Why do exothermic reactions release heat?

Exothermic reactions convert chemical energy (enthalpy) inside chemical substances into heat energy. The chemical energy decreases, and the heat energy increases (total energy is conserved).
We need to look in a bit more detail to understand why heat energy is produced from chemical energy during an exothermic reaction:
Any reaction requires the necessary bonds in the reactants to be broken – this requires energy to be supplied, so heat energy is taken in. We call this amount of energy the Activation Energy for the reaction.
Once the necessary bonds have been broken, the new bonds between the atoms in the products can be formed. BOND MAKING RELEASES ENERGY, RATHER THAN NEEDING IT TO BE SUPPLIED, so as a result of the bond making, heat energy is released.
In an EXOTHERMIC reaction, the amount of energy needed to break the necessary bonds in the reactants is LESS than the amount of heat energy released when the bonds in the products are made.
In an ENDOTHERMIC reaction, the amount of energy needed to break the necessary bonds in the reactants is MORE than the amount of energy released when the bonds in the products are made.