"The idea is trust in someone or something on the basis of their trustworthiness or reliability, their steadfast character."
"In the New Testament, when the Centurion comes to Jesus to heal his slave, he is asked why he came to Jesus: he did not know Jesus personally, so the obvious question is ‘why trust (have faith in, believe in) me?’ What is his response? He responds that because of Jesus’ reputation and His observed works, He is obviously one with authority over this issue: his faith is based on historical evidence (reputation and witness testimony) and direct observation. He didn’t come to Jesus with the attitude “Gee, I think I’ll try blindly believing this guy can help, and see if it works”: he came saying “I’ve heard about your works, I’ve spoken to people who have been there, and I’ve observed what you’re doing now: this tells me I am justified in asking you to do the same for my slave.” And Jesus describes this as ‘great faith’."
Now that sounds suspiciously like the way we use that word in the other areas of our life. This understanding is consistent with the definitions in the American Heritage Dictionary (2000), Webster’s Revised Unabridged (1998), WordNet (Princeton University, 1997) as well as the Easton Bible Dictionary, the Interpreter’s Dictionary of the Bible and other standard scholarly works both secular and religious.