Central City (often referred to as simply Central), is a city that is seated right in the middle of Amestris. It is the center of Government for Amestris, and is where Central Command, the National Central Library, and the 5 National Laboratories are located. Central is commonly referred to as Amestris' largest city and is metropolis-like, showing off the best technology Amestris has to offer.
A good amount of the Fullmetal Alchemist series takes place in Central, as it is where the military base is located, and also the location of the Homuculi's base, which is under Central Command.
Towards the end of the Brotherhood series on the The Promised Day, Roy Mustang leads an army, along with forces from East City and Briggs in order to overthrow the corrupt government because of Führer King Bradley's supposed death. As General Olivier Armstrong and Buccaneer come closer to success against Central, Führer Bradley makes his return and the battle becomes much more fierce.