An endergonic reaction in chemical thermodynamics usually produces a negative energy output and are low energy. Exergonic processes, on the other hand, usually produce a positive energy output and are high energy. An endergonic process, therefore, might be used to slow a chemical reaction down whereas an exergonic process might be used to speed up a chemical reaction.
In chemical experiments, for instance, the reaction starts out endergonic (or low output) up to a certain point (transition). The transition is where the reaction speeds up enough to reach the stable final product. This is an exergonic process.
Simple biological reactions may be too simple to proceed quickly on their own (endergonic process). But, when mixed with ATP, the reaction speeds up and becomes an exergonic process and the ATP is broken down, or decomposed, into simpler ADP (important in energy transfer between cells).
Both of these processes are important to the biochemical makeup and function of cells.