Endosymbiotic theory is the predominating explanation of how prokaryotic cells developed organelles and thus became eukaryotic, changing from very simple to very complex. It was proposed in 1981 by Dr. Lynn Margulis in her book Symbiosis in Cell Evolution, but wasn't taken seriously by the biology community for a few years. Previously, theory said that prokaryotic cells developed organelles as an ongoing evolutionary process, much as animals evolve physiology to suit their environment. Endosymbiotic theory suggested that at different points in time, known as endosymbiotic events, one prokaryotic cell actually internalized another, becoming essentially a new kind of cell with an internal support system.

It's important because it describes a major evolutionary step. Prokaryotes reproduce asexually, producing offspring that are identical to their parents. Eukaryotes were the first life to reproduce sexually and transmit shared advantages to offspring different from themselves. Since the original eukaryotes suddenly needed other eukaryotes to survive (ie, they were no longer strictly competing with each other), the possibility of multicellular organization opened up. Had endosymbiotic events never taken place, which they didn't for the first 2 billion years of prokaryotic life, none of todays multicellular plants or animals could exist.

Evidence for endosymbiosis is best seen in the mitochondria and chloroplasts of modern eukaryotic cells. Theory says that at one point the host cell and the mitochondrion were separate organisms. The host cell survived by absorbing other organisms, and the mitochondrian was an aerobic bacterium that survived by processing oxygen. At some point the host cell absorbed a bunch of the mitochondria, and they developed a symbiosis as the mitochondria absorbed cellular oxygen and left behind products that could be used by the host cell. Over time the mitochondria no longer needed much of the features they did as free-range organisms, and pared down their feature set accordingly, becoming truly an organelle of the host cell. When this same process happened with photosynthetic bacteria rather than aerobic ones, a chloroplast was the resulting organelle.

Since then prokaryotic DNA has been found for the centriole, an organelle responsible for cell structure and division. Evidently it too was once a separate prokaryote. Even though these three pieces of evidence basically validate the endosymbiotic theory, biology continues to look for prokaryotic DNA in the lysosomes, golgi apparatus, and sundry other organelles.

"But wait!" you're thinking to yourself, "What about the DNA? Aren't all of those organelles coded for in the nucleus?" Your question was the main sticking point for biologists opposed to endosymbiotic theory. They wondered how the absorbed cells' DNA could've possibly gotten out of them and into the host cell's nuclear genome. In the mid 80's, the mystery DNA was found right where you'd expect it to be, inside the chloroplasts and mitochondria. Better yet, it was circular, naked, prokaryotic DNA, wholly unlike the eukaryotic DNA in the host's nucleus -- visible evidence of the organelles once having been separate entities.

Interestingly, much of the proteins that make up organelles are actually coded by nuclear DNA. Current theory says that these are a product of evolution, since developing code for the organelles that could be evolved was of evolutionary interest for the eukaryotic cell. That is, since the eukaryote wanted (as much as a eukaryote can want anything) its organelles to evolve with it, it developed nuclear DNA replacements for the organelles' native DNA.