The Eight Corps of Baron is a term from the Final Fantasy IV Setting Data Book which refers to the whole of the army of the kingdom of Baron. It's so named because it's made up of eight different Corps, each one serving its own function.
The oldest Corps is the Personal Guard Corps, which was entrusted with protecting the King of Baron personally. It can be assumed that Baigan's ancestors were the head of this Corps because this Corps is made up of members whose heritage relates to it. Baigan is the captain of the Guard Corps.
The second Corps to be formed was the Dragoon Corps, which was founded by the ancestors of Kain Highwind. They were formed around the ability to fly Dragons into combat. They preferred to use lances over swords, although they were proficient in both. They preferred lances because of their long range ability. In Baron's early years as a nation-state, the Dragoon Corps was considered the most elite fighting unit, and Baron's most powerful weapon.
However, with the development of Airships, the Dragoon Corps began to fade out, and are relegated to castle defense, and only hard-line decedents of the original Dragoon Corps make up the fighting force. They still use lances for combat as a tribute, and many of them have learned to fly high in the air similar to dragons. Kain is the head of the Dragoon Corps.
The Dark Knight Corps included the most elite soldiers of the Baronian army, and only the truly gifted could become Dark Knights. Many try out to become Dark Knights, but the King personally selects all Dark Knights who are to enlist by decree. Training requires a mastering of the powers of darkness which must be mastered before combat. If someone unskilled in wielding the dark power tries to wield the Dark Sword, he will go insane and become evil. Cecil Harvey passed this test easily, and became one of Baron's best Dark Knights.
The Army Corps was Baron's standing army, made up of many of the lower ranked guards the player sees around the castle. The Navy Corps is not seen in the game, but it supposedly manned Baron's weak sea power. The Airship Corps was headed by Cid Pollendina and his ancestors, which designed airships for its most elite division: the Red Wings. The last two Corps only took form in recent history, as Magic began to develop. These are the Black Mage Corps and the White Mage Corps, which are made up of Black Mages and White Mages respectively. Rosa Joanna Farrell currently heads the White Mage Corps.