Usually rendered officially by George Lucas and company as "midi-chlorians," they were introduced to us in The Phantom Menace. They were mentioned by Qui-Gon Jinn as a biological cause (or perhaps a side effect?) of the Force. Qui-Gon has an exotic device for measuring the midi-chlorian count in blood cells. (It reminds me of the small device my dad uses to check his cholesterol count each morning.)
They are apparently microscopic entities, found within the cells of "all living things." It is not an unreasonable conjecture that they are organelles, sharing with those small entities the ability to congregate in numbers, and function, within a cell.
Qui-Gon claims that they are symbionts, and that without midi-chlorians, life could not exist. He even claims that midi-chlorians speak to the Jedi, whispering "the will of the Force."
One theory is that there are two schools of thought among the Republic's Jedi. Qui-Gon Jinn's school focuses on the living Force, which involves our microscopic topic. "Without the midichlorians, life could not exist and we would have no knowledge of the Force" says Qui-Gon. Yoda's school, which holds sway in the Jedi Council, stresses the unifying Force - the interconnection between all things. This does not seem to involve midi-chlorians. Perhaps Qui-Gon's odd theory makes him a pariah among the Jedi. Certainly it would explain why we hadn't heard of the little blighters in the 'second trilogy' of films, or even in Attack of the Clones.
I was moved to research midi-chlorians in more detail by a passing thought today. "If I ate a Jedi Master," I mused, "would my midi-chlorian count increase?"
At the time I was thinking that midi-chlorians might accumulate as you move up the food chain, rather like
certain toxins. It would be a wonderful basis for a plot twist in the second or third film.
I especially like this idea in combination with a theory I once read on this site, that the infamous Jar Jar Binks
was also very strong in the force, and that this accounts for his remarkable good luck where he is saved from
certain doom by a series of unlikely accidents. If he was indeed filled with midi-chlorians, Anakin and/or the Emperor might discover this and decide to, well, eat him.
This would be a suitably evil turn, and might resolve the burning question as to whether Jar-Jar tastes like chicken.
Sadly, based on the organelle theory, this does not seem likely. In such a scenario, midi-chlorians are likely host-specific, and could not be effectively transferred from one host to another.
A full discussion of biological theories around midi-chlorians as organelles can be found at:
http://www.theforce.net/midichlorians/index.shtml
Roninspoon says: incidentally, the device that Qui-Gon uses as communicator and blood tester is fabricated from a Gillette Lady Sensor razor.