What is a process within the cell of an organism that uses glucose and oxygen to produce carbon dioxide, water, and energy called?

It could be called oxidation (by a chemist), or metabolism (by a biologist). The body metabolizes glucose in various ways. See
http://www.carbs-information.com/glucose-energy.htm
The process is usually more complicated than you have indicated, with lactic acid or ATP as intermediate products.

The process you are referring to is cellular respiration. Cellular respiration is the process by which cells in an organism break down glucose and oxygen to produce carbon dioxide, water, and energy in the form of adenosine triphosphate (ATP).

To understand how cellular respiration works, you can start by learning about the different stages involved. The three main stages of cellular respiration are glycolysis, the Krebs cycle (also known as the citric acid cycle), and oxidative phosphorylation (also known as the electron transport chain).

1. Glycolysis: This is the first step in cellular respiration and takes place in the cytoplasm of the cell. During glycolysis, glucose is broken down into two molecules of pyruvate. This process also generates a small amount of ATP and NADH.

2. Krebs cycle: The pyruvate molecules produced in glycolysis move into the mitochondria. In the mitochondrial matrix, the pyruvate is further broken down through a series of reactions in the Krebs cycle. This process releases carbon dioxide and generates more ATP, NADH, and FADH2.

3. Oxidative phosphorylation: The final step of cellular respiration takes place in the inner mitochondrial membrane. The electrons carried by NADH and FADH2 are transferred through the electron transport chain, a series of proteins embedded in the membrane. As the electrons move through the chain, they release energy that is used to pump protons (H+) across the membrane. This creates an electrochemical gradient, which allows ATP synthase to produce ATP from ADP and inorganic phosphate.

Throughout the process of cellular respiration, glucose and oxygen are consumed to produce carbon dioxide, water, and ATP. It is important to note that the exact number of ATP molecules produced can vary depending on the conditions and the cell type.

To delve deeper into cellular respiration, you can explore reliable sources like biology textbooks or educational websites.