It's mainly the matter of personal experience)
As for Christianity I'd say to believe means to experience, to feel, to know as God is very personal. One may ask him and get the answer) Moreover, plenty of people throughout the history underwent a spiritual conversion by which they gained faith in God and became martyrs.

Well, it may be a little bit confusing... Just imagine your favourite banana)) Imagine, I've never tasted it and I ask you about its taste. You say, it's lovely. And I say, I don't believe you because once I've tasted a yellow fruit and it turned out to be sour. And I keep asking you for more facts to verify your judgement) Funny, isn't it?