According to the recent evidences, the eukaryotic cells with membrane-bound organelles originated by the process of serial endosymbiosis. According to this hypothesis, organelles such as mitochondria and chloroplasts originated when the symbiotic prokaryotes entered and lived inside other, free-living prokaryotic cells. For example, the evolution of double membrane-bound chloroplasts occurred when the photosynthetic bacteria (cyanobacteria) entered and lived inside the larger heterotrophic cells.
Likewise, the evolution of mitochondria occurred when the aerobic bacteria (most probably the purple bacteria) lived inside larger anaerobic cells. Gradually, the endosymbionts developed mutual relation with the host cells and the symbionts lost the ability to live freely outside the host cell.
They do the same thing that all living and breathing things do! They breathe! When they breathe they are doing the same thing you are doing all day everyday. Inhaling oxygen and exhaling carbon dioxide.
