Mitochondria are thought to have evolved from an engulfed alphaproteobacterium through endosymbiosis.
Under the endosymbiotic theory, an ancestral host cell took in a bacterial cell but did not digest it. Instead, the two organisms formed a lasting partnership: the bacterium supplied efficient energy production, while the host provided resources and protection. Over evolutionary time, many bacterial genes moved into the host cell's nucleus, leaving the mitochondrion dependent on its eukaryotic partner.
Mitochondria retain several features supporting this history. They have double membranes, their own circular DNA, and ribosomes that resemble bacterial ribosomes. They also reproduce by division, much like bacteria. These clues do not mean that modern mitochondria are free-living bacteria; they are highly integrated organelles.
Chloroplasts have a related but distinct origin involving ancient cyanobacteria. That distinction is a common source of confusion when comparing the evolutionary histories of mitochondria and photosynthetic organelles.