A midichlorian is a type of microscopic organism that lives inside the cells of all known creatures in the Star Wars universe, much like the mitochondria of the real world. The concentration of midichlorians in a person's cells correlates to that person's ability to manipulate the Force.
They are widely considered the stupidest piece of technobabble from the Star Wars franchise.
There is some debate concerning the cause-effect relationship between midichlorians and Force ability: it is unclear whether high midichlorian counts are the cause of Force ability or a result of it. The Jedi Knight Qui-Gon Jinn apparently believed the former, but he was widely regarded as a maverick within the Jedi Order, and his opinion on the matter did not seem to be popular with other Jedi Masters.