Endosymbiosis is an evolutionary theory which posits that eukaryotic cells arose from prokaryotic cells. The theory further articulates that the mitochondria found in today's eukaryotes evolved from aerobic bacteria and that the chloroplasts found in today's plant cells arose from cyanobacteria.
And the evidence would be the endosymbiotic theory is the fact that mitochondria and chloroplasts have their own circular DNA, prokaryote fashion, and can still replicate, transcribe and translate some proteins. Their ribosomes are also fashioned as a prokaryotes would be.