Gerald R. Van Hecke, a Professor of Chemistry at Harvey Mudd College, provides the following answer:
We can all appreciate that water does not spontaneously boil at room temperature; instead we must heat it. Because we must add heat, boiling water is a process that chemists call endothermic. Clearly, if some processes require heat, others must give off heat when they take place. These are known as exothermic. For purposes of this discussion, processes that require or give off heat will be limited to changes of state, known as phase changes, and changes in chemical constitution, or chemical reactions.
Changes of state involve a solid melting, a liquid freezing, a liquid boiling or a gas condensing. When steam, which is gaseous water, condenses, heat is released. Likewise when liquid water freezes, heat is given off. In fact heat must be continually removed from the freezing water or the freezing process will stop. Our experience makes it easy for us to realize that to boil water or any liquid and thereby convert into a gas, heat is required and the process is endothermic. It is less intuitive to grasp that when a gas condenses to a liquid, heat is given off and the process is exothermic.
Perhaps it is easier to explain an exothermic phase change using the following argument. Liquid water had to have energy put into it to become steam, and that energy is not lost. Instead, it is retained by the gaseous water molecules. When these molecules condense to form liquid water again, the energy put into the system must be released. And this stored energy is let out as exothermic heat. The same argument can be made for the process of freezing: energy is put into a liquid during melting, so freezing the liquid into a solid again returns that energy to the surroundings.
Like phase changes, chemical reactions can occur with the application or release of heat. Those that require heat to occur are described as endothermic, and those that release heat as exothermic. Although we are generally quite familiar with endothermic phase changes, we are probably even more familiar with exothermic chemical reactions: Almost everyone has experienced the warmth of a fireplace or campfire. Burning wood provides heat through the exothermic chemical reaction of oxygen (O) with cellulose (C6H10O5), the major chemical component of wood, to produce carbon dioxide (CO2), steam (H2O) and heat. The chemical reaction describing the process is C6H10O5 + 6O2 = 6CO2 + 5H2O + heat.
In today's space age, probably everyone has seen a rocket launch on television or, if lucky, in person. What powers those rockets are highly exothermic chemical reactions. One rocket fuel uses a mixture of solid ammonium perchlorate (NH4ClO4) and aluminum metal (Al) to produce a solid aluminum oxide, hydrochloric acid gas, dinitrogen gas, steam and heat: The chemical reaction can be described as 6NH4ClO4 + 10Al = 5Al2O3 + 6HCl + 3N2 + 9H2O + heat.
The great billows of white clouds seen behind launched rockets are really the product gases dispersing the white aluminum oxide powder. Where is the exothermic heat energy coming from? The heat comes from the energy stored in the chemical bonds of the reactant molecules--which is greater than the energy stored in the chemical bonds of product molecules. In endothermic chemical reactions, the situation is reversed: more chemical energy is stored in the bonds of the product molecules than in the bonds of the reactant molecules.