The word faith in English has various uses, but its central meaning is equivalent to "unconditional trust or belief." As such, the object of faith can be either a person (or even an inanimate object or state of affairs) or a proposition (or body of propositions, such as a religious credo). In most contexts, "faith" means religious faith, that is, unconditional trust or belief either in the (presumably existent) God of one's religion, or that some religious tenets are true. It is in the latter sense in which one can speak of, for example, "the Catholic faith" or "the Islamic faith."
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.
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.