Mitochondria are covered by a double membrane. The inner membrane contains the ATP-Synthase, the enzyme that makes ATP using the H+ gradient created by the proton pumps of the respiratory chain. Its surface is massively enlarged by protrusions („cristae“). Between the two membranes there is an intermembrane space, where the H+ gradient is stored. The inner membrane covers the matrix, which contains the mitochondrial DNA and ribosomes and where the citric acid cycle takes place.
The larger the inner membrane surface the more ATP synthases can be located there and the more ATP can be made by them.
Mitochondria is very important, because it enables the full oxidation of energy sources like carbohydrates and sugars, so that a maximum of energy (as ATP) can be obtained from them. For example, in fermentation ATP is only made during glycolysis (4 per glucose molecule), whereas in the full oxidation to H2O ca. 32 ATP are made :)
