Simply put, Nicolaus Copernicus' major accomplishment was developing and advancing a mathematically supported theory of heliocentricism. Previously, Ptolemy's geocentric theory, which placed Earth at the center of the universe, was the most widely accepted model for the organization of astronomical bodies. Although Copernicus' theories would not be widely accepted during his lifetime, they would later be studied and improved on by other astronomers. As such, he is often referred to as the father of modern astronomy.

Copernicus was very skilled in mathematics and scientific observation. He based his conclusions on what he could actually observe, eschewing ideas that were handed down as truth without evidence. He noticed a number of inconsistencies with the Ptolemaic model of a geocentric universe. By relying heavily on repeatable observations, Copernicus was also breaking new ground in the field of scientific study. Later scientists, such as Kepler, Galileo, and Newton, would follow his example and also place great importance on drawing scientific conclusions based on observation. This would eventually develop into the scientific method.

Copernicus published his conclusion in his astronomical treatise called On the Revolutions of the Celestial Spheres. He even dedicated this work to the pope when it was published in 1543. However, because his heliocentric model contradicted the teachings of the Church, his book was added to the list of forbidden works by the Catholic Church in 1616. However, astronomers still used it as inspiration and the basis of their celestial observations throughout the Scientific Revolution. Today, it is still considered one of the foundational texts of modern astronomy.

Nicolaus Copernicus was a 15-16th century astronomer and mathematician. Copernicus was a true "Renaissance man"; in addition to being proficient in mathematics and astronomy, he was fluent in multiple languages, studied and translated ancient works, practiced church law and medicine, and served as a political diplomat.

Copernicus' greatest accomplishment was his famed work, On the Revolutions of the Heavenly Spheres. In this work, Copernicus proposed a heliocentric (sun-centered) model of the universe, which contrasted with the prevailing geocentric (earth-centered) view. Unlike Galileo, Copernicus did not mandate the scientific community accept his system as truth; rather, he merely presented it as a system which could successfully account for observable physical phenomena. 

Copernicus' theory was slow to catch on, but it began to gain notoriety after Galileo asserted that the earth and the other planets revolved around the sun. This theory is credited with helping to spark the Scientific Revolution.