In general a special-purpose district is a government district like a municipality, county, etc. (general-purpose districts), but for a special purpose only. A good example of a special-purpose district would be a school district. Special districts are sometimes created to provide fire protection or sewerage, or to manage water resources. These districts are usually much more flexible than more geographically determined municipalities.
There are two types of special-purpose districts. Some are independent, in that they are allowed to tax, and others are dependent in that they receive funding only from user fees or from other governments.