For Christians [and others?? I've no idea], one typical understanding of the meaning of "faith" has it that, if one has faith in something (such as the existence of God), one's belief is claimed not to have any specific evidence or arguments. In other words, there is nothing about the belief itself that makes it an instance of faith, but rather, it is how that belief is related to other things one believes, that makes the belief not just any belief, but faith. In particular, on this view, what makes a kind of religious belief not just belief, but faith, is the fact that the belief is not supported by arguments, or reasons, or evidence. Or most generally: there are no other beliefs that one has, which one thinks makes one's belief in some religious tenet more probably true.
This is probably too extreme an account of what faith is; it is, at least, also common to regard faith as belief in a thing without adequate or overwhelming evidence or arguments.
There is a very wide variety of views about the role of faith in religion. One view, fideism?, has it that one ought to believe that God exists, but one should not base that belief on any other beliefs; one should, instead, accept it without any reasons at all. There are some kinds of moderate fideism which say that one should have faith to begin with, and only then, when one's faith is strong enough, go out in search of reasons to believe--this latter is a [very rough!] statement of the view of Thomas Aquinas. Like Aquinas, nearly all Christians believe that some amount of faith is necessary in order to be a believer.
Soren Kierkegaard is an example of a radical fideist; his views are presented in [Fear and Trembling]?.
This still needs a lot of attention from a theologian or several! It also needs more about the very notion of faith in religions other than Christianity.
See faith and rationality, Scientific method.
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