The year 1905 is referred to as annus mirabilis ("miracle year") because it is the year in which Einstein introduces the theories that make him famous at the young age of 26.
First, in his Special Theory of Relativity, he demonstrates that space and time are not absolute but vary with the proximity of one object to another.
Example; for a person living in orbit around the Earth, time would pass more slowly than if he/she were living at sea level. The difference is not great, but it is still there and this is due to the variance in gravity with respect to earth.
This would mean Isaac Newton was wrong, although his theories still generally hold for calculating dynamics close to Earth.
Also, Einstein takes on the topic of light and by the time he publishes the paper he has given light (photons) particle-like properties AND wave-like properties.
Second, Einstein comes up with the quantum theory of light which is the idea that light is made up of tiny particles (now called photons). Combining his work with Planck and Bohr, Einstein introduces the idea that the universe is made up of tiny bits of energy and matter.
Third, Einstein produces two papers which in combination is a proof of the existence of atoms.
Fourth, an edition to special relativity proves a link between energy and matter (Energy is equal to mass times the speed of light squared).
These theories were quite shocking at the time. They also began to paint a picture of what the universe is like and the fascinating phenomena that occurs. Einstein certainly did have a "miracle year".