What is the “symbiotic theory” and how does it fit in with cells?

Symbiotic theory's main idea is that simple prokaryotes evolved into complex eukaryotes.
The way this evolution processed is curious: when prokaryotes ate each other, the ones which were eaten, did not die, but instead changed into organelles like the nucleus, mitochondria etc.
The fact which supports this theory is that mitochondria have their own DNA different then DNA of the DNA of the creature.