The clear separation of religion and state is the basis of all rational thinking. After all, who can consider developing empirical evidence-based research when all his superiors continue to believe blindly in whatever the Church tells them to believe? And so, Secularism enables all specialists in your cities to aid scientific progress through developing critical thinking.
This is one of the most powerful Science boosters in the game, particularly for empires with lots of specialists. The interesting part is that the type of specialist doesn't matter; they all get a bonus +2 Science to their output (which comes alongside their regular output, so for example an Engineer specialist produces +2 Production and +2 Science, while a Scientist specialist produces a combined +5 Science), and this bonus gets increased further through scientific buildings in cities. So, the more Specialist-oriented your empire is, the greater and more immediate is the effect of this Policy, regardless of what Specialists are you concentrating on.
Secularism is the belief that government should be separate from religion and religious faiths. Religions should not be taught in schools, nor should one's religion determine whether he or she can work in the government or serve in the military. Secularists don't necessarily disbelieve in a Supreme Being; they just think that mixing religion and government is ultimately bad for both institutions. The United States is largely a secular country, although traces of its early inhabitants' dominant religion can still be found on the country's money, its leaders' oaths of office, in its judicial system, and so forth, often to the dismay of the citizens who do not belong to that religion.