The idea that faith means belief in the unverifiable or "Believing what you know ain't so" is largely the invention of modern religious thought in the face of scientific knowledge shrinking the space in which the God Of The Gaps can exist. Throughout most of history of Abrahamic religion, the idea of the Abrahamic God's unverifiability would be nonsensical -- theologians went to elaborate lengths to construct logical and philosophical "proofs" of God's existence or various true statements about God's nature, and the idea that such truths are somehow invalid because they're just thought experiments not backed up by empirically verifiable physical experimental evidence is, itself, an anachronism if you assume it's in place before the ascension of the formal scientific method in use today. For a long time, logical proofs were considered more sound than experimental proofs, not less so.
Faith means trust. It is literally a synonym for trust. Hence "Breaking faith" as a synonym for betrayal or reneging on an agreement.
Having faith in a god means having trust they'll hold up whatever end of the bargain you've been taught they've made with you or your culture.