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Symbiosis: two organisms live closely together

Endosymbiosis: one organism lives inside another (like bacteria live inside of us)

It is thought that chloroplasts and mitochondria were originally free-living prokaryotic cells which gradually became able to live and reproduce within a larger cell. The larger cell provided protection and in some cases food to the prokaryote, while the smaller prokaryotic cell (which became the chloroplasts & mitochondria) provided an energy supply to the larger cell.

Evidence:

a. mitochondria and chloroplasts surrounded by double membrane

b. mitochondria and bacteria have similar size

c. mitochondrial ribosomes resemble bacterial ribosomes

d. mirochondria and chloroplast DNA is circular like bacteria

e. mitochondria divides by simple fission like bacteria

Wikipedia: Theory of Endosymbiosis

Discover Biology, 3rd Ed: Animation of Theory of Endosymbiosis