The space within the cristae is called the "matrix".
The space between the outer and inner membranes is called"intermembrane space."
Synthesize ATP, the cell's energy currency.
Via the citric acid cycle and oxidative phosphorylation, which is the coupling of two reactions: the oxidation of nutrients and the phosphorylation of ADP.
They have electron transport chains and enzymes embedded in their inner membrane, which facilitate these reactions.