A mechanism is a description of what is actually happening in a reaction at the molecular level. If we think a reaction as a recipe, the reaction that we are used to writing (the one that we do stoichiometry problems with) is what is found at the top of the recipe card—the ingredients and the yield.
Image recipe1 (recipe with highlighted sections)
The mechanism is all of the stuff underneath that tells you what you have to do. Sometimes that is very simple: Mix together. Eat. Sometimes it is much more complex: Mix the dry ingredients. Separate the eggs. Beat the egg whites. Etc.
Reactions mechanism can also be simple or complex. Many reactions occur in one step (Mix and Eat), but others occur in two or more steps.
The graph that represents the energy of a reaction can thus appear somewhat different for a reaction that occurs in multiple steps.
The question then is why do mechanisms matter?
The NO2 and Co mechanism explains the basics of mechanisms and the ozone mechanism discusses how human activity added a catalyst to the upper atmosphere and its impact on the ozone layer.