In the United States, we use the term “local government” to refer to the lowest level of government. This is the government of our own town or our own county.
In the US political system, we have multiple levels of government. At the top, we have the federal government. This is the government that is centered in Washington, D.C. At the next level, we have the governments of our individual states. Depending on where we live, we will also have a county government and, perhaps, a city government. (Some people live in unincorporated areas that have no city governments.) We refer to the lowest level of government as our “local government.” This is because it is the government that has only to do with our own locality.