The Society of Jesus is more commonly known as the Jesuit order. It is one of the largest religious orders in the Catholic Church. The Society of Jesus was founded in 1540 by St. Ignatius of Loyola, a soldier from Spain. Ignatius called the organization "the army of Jesus."
The Jesuits are known for their loyalty to the Pope, and even take a special vow of obedience to the Pope. Because of this, the Jesuits took a leading role in the Counter Reformation, defending the Catholic Church from the "errors" of Martin Luther's Protestant Reformation (though this was not the society's original purpose).
In the 16th, 17th, and 18th centuries, the Jesuits' schools and scholars were so reknowned that the Jesuits were called the schoolmasters of Europe. Their popularity and influence with the pope, however, gained them many enemies. In 1773, Pope Clement XIV yielded to pressure from the French and Spanish courts, and ordered the disbanding of the order.
After the Supression, the schools of the Jesuits had to be turned over to governments and other institutions. Many of the Jesuit books and other scholarly works were lost because of this. 41 years later, the Supression was lifted, and the Jesuits continued their mission. Many of the schools were reverted back to the Jesuits.
In the Modern era, the Jesuits have remained very active. They have established a worldwde school system, today there are about half a million students being taught under the Jesuits. In the field of science, perhaps the most prominent Jesuit scientist was the paleontologist Pierre Teilhard de Chardin. The Jesuits have been active in the political realm as well, speaking out against unfair social structures in Latin America, for example.
It is no surprise that the Jesuits, founded as a military order, are very good at logistics, and are people of action. Fidel Castro was educated by the Jesuits, and he had once proudly said that he was a "Jesuit boy." Perhaps that is why one of the first things he did when he got into power was ban the Jesuits from Cuba.
More info and references:
http://www.fairfield.edu/jesuit/history.htm
http://www.newadvent.org/cathen/14100a.htm