Bonds, as we know, can be covalent or ionic. Regadless of which type of bond we are dealing with, we know that the bonds are just attractions between atoms or ions. We also know that when two attracted things are separated they have potential energy. As they come closer this potential energy goes down; as they are separated, the potential energy goes up. We also know that energy is conserved, that is energy is not created or used, only transferred.
Putting those ideas together, we can realize the following:
When a bond is made (when attracted atoms or ions are brought together) their potential energy goes down. This requires that some energy is given off.
Conversely, when a bond is broken (when two attracted atoms or ions are pulled apart) their potential energy goes up. This requires energy to be added for this process.
The amount of energy given off when a bond is formed (or taken in when the bond is broken) is called the bond energy.
It is this idea that explains why all reactions require some energy to start them and why all reactions give off some energy. It also explains why some reactions are exothermic (overall) and some are endothermic (overall).