The State Military is the the group of soldiers that protects Amestris or the armed forces. Since Führer Bradley is the king of Amestris, he subsequently became the commander-in-chief of the military.
The State Military contains both soldiers and State Alchemists. State Alchemists are people who are trained in Alchemy and decide to join the military. These special soldiers are automatically given the rank of a major, and are treated as such by all soldiers with a lower rank. The Amestris State Military is said to have one of the most powerful military powers in the entire world of Fullmetal Alchemist, simply because of its profound use of Alchemy alongside its soldiers.