Secular is an adjective used to describe things or people that are not religious.
When Grand Ayatollah Ali al-Sistani, the most influential Shiite cleric in Iraq, spoke out a week ago, calling for full national elections instead of the caucus-style balloting envisioned in the American plan for self-rule, most secular politicians concluded that he hoped the voters would elect a theocracy. (NY Times)
Residents of Jerusalem chose a secular businessman to lead one of the world’s most revered and complicated cities, putting an end to five years of ultra-Orthodox Jewish control, election results showed Wednesday. (USA Today)