City and Village Councils (full title is: Provincial, City, District and Village Councils) are local councils which are elected by public vote in all cities and villages throughout Iran. Council members in each city or village are elected by direct public vote to a 4-year term.
According to article 7 of the Iranian Constitution, these local councils together with the Majlis (Parliament) are "decision-making and administrative organs of the State". The councils are in charge of electing mayors, supervising the activities of municipalities; study of social, cultural, educational, health, economic, and welfare requirements of their constituencies; the planning and coordination of national participation in the implementation of social, economic, constructive, cultural, educational and other welfare affairs.
Iranian Constitution Article 7: http://www.iranologyfo.com/low-e01.htm
Overview of Iranian Political System: http://www.irtp.com/howto/partner/partner/chap1/chap1v.htm
BBC News: Iran prepares for first-ever local elections: http://news.bbc.co.uk/hi/english/world/monitoring/newsid_276000/276816.stm
BBC News: Iran's women show political muscle: http://news.bbc.co.uk/1/hi/world/middle_east/289503.stm
Article in The Iranian: http://www.iranian.com/Features/2003/February/Council/