How did cells get the first mitochondria

The theory of endosymbiosis explains this. It is basically the idea that billions of years ago, a relatively large prokaryotic cell engulfed another, smaller prokaryotic cell. This prokaryotic cell had the ability to convert organic fuels into ATP, or a form of energy cells could use. Over time, these cells developed a symbiotic relationship, and the smaller prokaryotic cell developed into the first mitochondria, which share the same function of producing cells' main forms of energy currency.

The endosymbiotic relationship of mitochondria with their host cells was popularized by Lynn Margulis. The endosymbiotic hypothesis suggests that mitochondria descended from bacteria that somehow survived endocytosis by another cell, and became incorporated into the cytoplasm.