Faith-based means built on religious belief — a church, a temple, a god, a tradition — rather than on a government rule or a lab result. You meet it most in the phrase faith-based organization: a charity, school, or hospital that grows out of a religious group. The term faith-based organization is recorded from 1971, and the political use grew through the 1970s and 1980s, especially in the United States: should public money go to groups like that, and with what limits? It sounds official. It does not name one religion. A faith-based hospital may treat anyone; the “faith” is in who runs it and why. Though actually, people sometimes stretch faith-based to mean “we believe this without needing proof,” even outside religion. Strictly, the word points at religion. “I have faith in you” (I trust you) is a different faith. The hyphen is doing real work: based tells you what the ideas or the group sit on.