Endosymbiosis is where two organisms live together, one inside the other: endo=in, sym=together and biosis=living.
It is believed that mitochondria originated as eubacteria that were intracellular parasites of the early anaerobic eukaryotes. Evidence for this is primarily found in the mitochondrial genome. It has been sequenced and compared to many other species of bacteria and similar organisms have been found. Other data that support this is the presence of a double membrane around mitochondria, as if the original eubacteria were endocytosed. In addition mitochondria have their own ribosomes to make proteins encoded by their genomes.
The 'pro-mitochondria' received glucose from the anaerobic eukaryotes and the anaerobic eukaryotes received a much greater amount of ATP (the main energy 'currency' of life) courtesy of the mitochondrial aerobic respiratory chain.
Though once a free living organism, it is wrong to think of the mitochondria now as 'other' or as an independent entity. Evolution has robbed it of most of its genome; the human mitochondrial genome has just 13 proteins encoded in it and as a result many of the proteins and in some cases small RNA molecules must be transported into the mitochondrion after being transcribed from the nucleus and translated by the rER.
Interestingly when the sperm and egg fuse in fertilisation, it is primarily the maternal mitochondria that are encorporated into the zygote and as a result mitochondrial diseases are inherited maternally, for example MERRF syndrome. Intuitively the tissues worst affected are those with high oxidative demands.
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