Short answers, pulled from the story.
The annus mirabilis papers are four scientific papers Albert Einstein published in the journal Annalen der Physik in 1905. They addressed the photoelectric effect, Brownian motion, special relativity, and mass-energy equivalence. Together with quantum mechanics and general relativity, they are considered the foundation of modern physics.
Einstein's photoelectric effect paper, received on the 18th of March 1905, proposed that light energy travels in discrete packets called quanta rather than as a continuous wave. It was the only specific discovery cited when Einstein was awarded the Nobel Prize in Physics in 1921.
Einstein's second 1905 paper derived expressions for the mean squared displacement of microscopic particles in a liquid, giving experimenters a method to count atoms using an ordinary microscope. The work helped convince scientists, including former atom-skeptic Wilhelm Ostwald, that atoms were real physical entities rather than a theoretical convenience.
Special relativity rests on two postulates introduced in Einstein's third 1905 paper. First, the laws of physics are the same in any non-accelerating frame of reference. Second, the speed of light in empty space is the same for every observer, regardless of the motion of the emitting body.
The equation states that the energy of a body at rest equals its mass multiplied by the square of the speed of light. It appeared in a paper published on the 21st of November 1905. Einstein showed that if a body radiates energy, its mass decreases by a corresponding amount, a relationship that later explained why nuclear reactions release enormous amounts of energy.
Einstein was working as an examiner at the Patent Office in Bern, Switzerland, in 1905. He had limited access to scientific reference materials and few professional colleagues to discuss his ideas with. He later named Michele Besso, a co-worker at the Patent Office, as the best sounding board for his ideas in all of Europe.