The free exercise clause refers to the free exercising of religions in the US by the US citizens. This means that the citizens themselves have the right to choose the religion they want to exercise, without influence of the Government.
The Free Exercise Clause of the First Amendment pronounces that the state "shall make no law, preventing the free practice of religion." Although the line seems simple, "no law" does not regularly express "no law." The Supreme Court has had to put some boundaries on the liberty to exercise religion.