When World War II broke out, the Allies had been formed to stop HYDRA's goal of world conquest. In the early years of the war, HYDRA had nearly took half of Europe and other parts of the world, forcing the Allies to retreat and hold their remaining ground.
Desperately in turning the tide of war, the Allies had initiated the Operation Rebirth which creates supersoldiers from the Super Soldier Serum made by Dr. Abraham Erskine. The operation was sucessful, the Super Soldier Serum had transformed their test subject, Steve Rogers, who will be known as Captain America. But the sample of the serum was lost and Erskine had died, leaving Cap the only true super soldier.
On a raiding mission on Norway, Captain America and Bucky had led the Howling Commandos to get past HYDRA's core defenses and into the Red Skull's fortress. Once Captain America and Bucky were inside, the commandos stayed behind to secure the outer perimeter.
As Cap and Bucky disappeared in the Artic Circle, the Allies (including the Howling Commandos) had grieved for their "loss" and decided to finish this war and take down HYDRA for the two heroes. On the final years of the war, the Allies had won against HYDRA, from which its remains went into hiding for decades until to the present day.
After the Second World War had ended, the Allies had disbanded and the United Nations and S.H.I.E.L.D. are its current sucessors as the symbols of peace and order.