HYDRA is the branch of the Nazi-Germany Army of World War II under the command of Johann Schmidt. It was an SS sub-division that created advanced weaponry for the army.
Their main purpose was to create advanced weapons for the Nazis. They stormed a castle in Norway where the mystical object known as the Tesseract was buried for hundreds of years. They used the power to create advanced technology weapons and tanks. After discovering such power, Schmidt separated from the Nazi-Germany army and created their own Super-Army to rule over the world. HYDRA had many bases around Europe but the US Army sent the SSR team with Captain America and the Howling Commandos to destroy the HYDRA factories. Then, after Schmidt died, HYDRA was dissolved and its advanced technology was studied by Stark Industries.