“Incorporation” is perhaps not the ideal word to describe this, but for reasons rooted in legal history it’s the one that’s used. Every actual city (or town, village, etc.) with a municipal government is a “municipal corporation” created or authorized by the state in which it lies. The powers of an incorporated municipality are those delegated it by the state, and can be fairly wide ranging. But in general they include planning and zoning, the ability to bond for municipal improvements, the right to run a police department, a fire department, a public works/streets department, water and sewer services, etc. All the normal things which one thinks of with reference to his or her home town. Each state has a section of the state legal code devoted to how to run a city, how to run a town, etc., and specifying what it can and cannot do.
In general, an unincorporated municipality has no powers; it’s merely an area of populated land known by a given name. There may be states in which this generalization is incorrect, though. One thing that is a common character of an unincorported place is that it’s organized into a local fire district, which has the power to levy taxes or to have the county levy taxes, to support its operation. (Not the fire company itself, which is generally volunteer, but the cost of the fire trucks, the fire house in which they are housed, EMT/heavy rescue vehicles, training programs not funded by the individual or the state, etc.)