Parish councils are the lowest tier of government in England. They are no longer anything to do with the church, although they were in times past. The parish council is responsible for a parish, a small area normally enclosing one community. If the community is sufficiently large the council may be called a town council, rather than a parish council but its responsibilities and powers are identical. In some small parishes there is no parish council, just an annual general meeting.
The next tier above parish councils is the district council, which covers a much wider area, and above that comes the county council. As town councils sometimes exist as an alternative to parish councils you sometimes find city councils in place of district councils, Cambridge City Council being an obvious example.
Not every community has a parish council. In Cambridge for example there are none. Finally, the last re-organisation of local government introduced the concept of unitary authorities combining the function of district and county councils. Peterborough is an example of this.
The parish can get money from its residents in the form of a "precept", which is added to the figures requested by the county council, the police and fire authority and the district council and is then collected by the district council in the council tax (previously called the community charge or "poll tax" and, before that, the rates).