This lesson makes the point that spontaneous chemical reactions (reactions that go by themselves) are like borders rolling down a hill. They go toward greater stability (lesser potential energy). Therefore, energy is given off in the process. The burning of carbon (charcoal,) is a prime example, C + O2 —> CO2 + energy.
The text gives the baking soda-vinegar reaction as another example. This is an error. This particular reaction actually absorbs energy making the reaction container feel cooler. This is not an exception to the rule — it involves two coupled reactions — but the explanation is long and complex. It will be best to omit this reaction from discussion.