The Jesuits (officially, the Society of Jesus) were formed as sort of an elite order of Catholics who would dedicate their lives to promoting and preserving the Catholic faith. They were particularly interested in combatting the Protestant Reformation that was going on around the time that they were founded.
The Society of Jesus was founded in 1540. It was created by a man named Ignatius Loyola who had been a soldier but who had turned to religion while recovering from a wound. He received permission from the pope to start a new religious order that would be directly responsible to the pope (as opposed to local bishops).
The major role of the Jesuits historically has been as missionaries and educators. For example, I started my high school career at a Jesuit school in Micronesia.
Here is a relevant quote from the link I've attached:
As the object of the society was the propagation and strengthening of the Catholic faith everywhere, the Jesuits naturally endeavored to counteract the spread of Protestantism. They became the main instruments of the Counter-Reformation; the re-conquest of southern and western Germany and Austria for the Church, and the preservation of the Catholic faith in France and other countries were due chiefly to their exertions.