The secular and religious states may not have much debate today, but before the American Revolution, it was a heated debate between citizens and politicians. People who want the state to support a religion often want the head of the state (typically a monarch or dictator) to hold the values of a religion, and support it through policy. Advocates of a secular state do not want religion in any government, and support tolerance of all religions.
Most of the countries today push secularism because of Enlightenment ideals spread in the 18 and 19th centuries. Countries in the modern world make sure that people have the freedom to practice whatever religion they please, as long as it is not harming other individuals. This may not sound radical to the average person in the 21st century, but basically all of Europe and Asia was founded on Theocracies. In Europe it was mainly Catholicism or Orthodox Christianity, while in Asia it could be Confucianism, Hinduism, or Buddhism. The switch from these theocracies into religiously free places was a dramatic shift in governmental policy.
There are a few countries that still are not secular, most of them in the Middle East. Iran is one of the biggest ones to have religion in government, as the Islamic Shah controls the country. The Shah is a religious and governmental ruler, and has laws that are directly influenced by the Qur'an and Islamic faith. The other big non-secular state is Saudi Arabia, which has Sharia Law in it's laws, making it so that women have to be covered when they go out in public, and heresy against Islamic faith is prohibited.
Theocracy is not limited to Islam, though that is the best example in today's world. To some extent, the Democratic People's Republic of Korea (North Korea) could be considered a theocracy, as it's laws protect the Cult of Personality around Kim Jong Un. Historical examples can be found everywhere, even in Mesopotamia in the first civilizations. Theocracy typically has a negative connotation in America, but the stability and unifying factors of a religious state can not be discounted. There are always benefits and detriments to every type of government, and to remove bias and look at things objectively, you can start to critique the time period you live in, and the government you live under.