Religion plays a very central role in Iran, both in politics and in society at large. Iran is ruled by a supreme council of religious leaders (Ayatollahs). Even the prime minister, Ahmadinejad, must answer to this supreme council. Many outside political observers believe that Iran's elections have been manipulated by the supreme council and/or its agents.
Iranian citizens heed the call to worship five times per day, as is customary in Islam, yet continue to embrace many Western concepts, including the internet, music and clothing (especially jeans).
Iran is an Islamic theocracy with most of its laws based on Sharia law of that religion. Iranian imams (clergy) can overrule/override secular legal decisions.
Judaism is the religion of the Jews, it is not a government.
There is no king of Iran. There is the spiritual leader, called the Ayatollah. Since Iran is a theocracy they follow a religion, as their government. The current Ayatollah of Iran is Ali Khamenei.
In ancient days religion had played the role of government. Government is the modified form of religion due to transition in civilization.
The majority religion in Iran is Shi'ite Islam.
The term that best describes a government based on religion is called a Theocracy (Theo meaning God).
A theocratic government is one where the Religion and the State are the same - that is, all government functions (and decision-making) is done by the religious hierarchy. This is distinct from the concept of a State Religion. Currently, there are really only one real theocracy in the World: Vatican City. Iran has a strange mix of theocratic and democratic elements. Likewise, Saudi Arabia has a mix of theocracy and an absolute monarchy. Israel has a State Religion with some influence over the secular government, but even that portion really isn't a theocracy (as the State Religion isn't organized in such a manner as to be able to exert institutional influence).
Iran is a theocracy, which means that religion has a large if not central role in governance. Currently, Iran styles itself as an Islamic Republic, meaning that Islam is central to the governance and control of the country.
the role was big because it affected how the government worked
Yes for example in Iran you must follow Muslim religious rules even if you are another religion.
That is currently happening. Several governments limit the freedom of religion. As an example, in Iran, if you change your religion (from Muslim to something else) you can get executed for "apostasy".
the things they say is that they cant effect religion
The government allows several specific churches, but conversion from Islam to another religion is prohibited.