In democracies power is divided into 3 branches:
Legislature: responsible for creation of laws, and adjusting old ones to the changing situation.
Executive: has the authority for the daily administration of the state.
Judiciary: courts, tribunals, which make sure that law and constitution are being obeyed.
Power is also shared vertically (central-local).
In some countries power is centralised, current government manages what is going on in the country on all levels, and prepares plans and grants funds even for local investments.
On the other hand there are countries (like USA) where local authorities, in addition to the management of funds, are responsible even for legislature and have their own laws.
In some countries part of the local budget is reserved for direct vote of the citizens. They decide if they want a new swimming pool, liberary, improvement of roads and so on. Internet and qulaified electronic signature made this kind of vote possible.
Power can also be shared between different nations within one country (like in Belgium, or in Bosnia, where there are 3 officials for most offices. They have 3 prime ministers Serbian, Croatian and Boszniak). It makes sure that the minorities will also have a say in the process of law creation.
