Most of the metabolic activity in a cell occurs in the mitochondrion. This organelle is responsible for the generation of ATP through a process known as oxidative phosphorylation.
Both fatty acids and carbohydrates are metabolized inside the mitochondrion. The purpose of this breakdown is to produce as much ATP as possible through the process of glycolysis and the citric acid cycle. The ATP is then used to fuel other processes occurring in the rest of the cell.
The mitochondrion is a unique organelle as it has its own variant of DNA. This allows the organelle to produce its own proteins, tRNAs and rRNAs. It is thought that mitochondria originally began life inside bacterial cells, but transferred to complex eukaryotic cells later on. This is known as the endosymbiotic theory.