The key to the success of eukaryotic cells are two powerful, mutually supportive organelles: the mitochondrion and the chloroplast:
The mitochondrion consumes oxygen to efficiently extract energy from carbon sources like glucose, producing carbon dioxide and water in the process.
The chloroplast consumes water and carbon dioxide as it captures energy from light and funnels it into the chemical energy of glucose, releasing oxygen in the process.
Endosymbiotic theory proposes that these organelles were once prokaryotic cells, living inside larger host cells. The prokaryotes may initially have been parasites or even an intended meal for the larger cell, somehow escaping digestion.
Whatever the cause of their initial internment, these prokaryotes might soon have become willing prisoners to a grateful warden. The prisoner prokaryotes might have provided crucial nutrients (in the case of the primitive chloroplast) or helped to exploit oxygen for extracting energy (in the case of the primitive mitochondrion). The prokaryotes, in turn, would have received protection and a steady environment in which to live.
Multiple lines of evidence support the endosymbiotic theory. Endosymbiosis is observed elsewhere in biology. Mitochondria and chloroplasts have intriguing similarities in structure, reproduction, biochemistry, and genetic makeup to certain prokaryotes. The plain fact that mitochondria and chloroplasts have any genetic information of their own argues in favour of the theory.
Because virtually all eukaryotes have some sort of mitochondria, while only photosynthetic eukaryotes have chloroplasts, it has been proposed that endosymbiosis occurred twice, in series. First, an aerobic (oxygen-using) heterotrophic prokaryote was taken in by a larger host cell. In time, the prokaryote co-evolved with the host, eventually becoming something like a mitochondrion. Next, a photosynthetic prokaryote was taken in by a mitochondrion-containing cell. This model of eukaryote origins is called serial endosymbiosis.