We are first introduced to the Jem'Hadar in the episode of the same title in season #2. We learn they are the puppet warriors for the Founders, the tyrannical race of beings who dominate the Gamma Quadrant.
The Founders, who we later learn in season #3, are Changelings and Constable Odo's long lost relatives. They use and breed this specialized army for the purposes of intimidation, killing, and expanding the Founders stranglehold on the hapless inhabitants of the quadrant.
The Jem'Hadar are not only bred with the characteristics of loyalty to the Founders, but are kept in line with a special drug called Ketracel White. It contains addictive properties and also acts as food.
The warriors are taught that victory is life, even if it means their death. They remind me a lot of the Klingons, with a warrior mentality and a sacred call to battle in the name of honor. The Federation was at their mercy only as far as the Founders were willing to take the war.
One in a while a band of Jem'Hadar would go rogue, as they did in "Hippocratic Oath." Their leader demanded of a captured Dr Bashir to help them discover a way to rid them of their dependence on the White. That was not successful.
The Jem'Hadar are the creation of The Founders, Changelings who exist primarily in "the great link," as one liquefied unit. They can become individual units ("solids") and did so many times during their occupation of the Gamma Quadrant.
We meet them in "The Search," and their matriarch, when solid, explained to Odo that they became conquerors after thousands of years of being tormented and hunted by solids who feared them. They decided to strike back and become the biggest threat to the solids in the Gamma Quadrant.
Their leader eventually surrenders to the Federation after they are outmaneuvered and the great link is suffering from a deadly contagion invented by Section 31. The virus made it impossible for the Changelings to change shape once they were infected. Those that remained in the great link were unable to participate in the war and their leader could not join the link due to being stuck in solid form. Upon surrender, she was cured by Odo who had within him the vaccine. He then carried it to the great link.