In a sense, one could argue that what defines faith is that it does not have a foundation. One normally would not describe a belief based on evidence or observation as faith; instead, faith is belief in the absence of external warrants.
In a religious context, faith is an important characteristic of many modern monotheistic religions, but was a less important feature in earlier polytheistic religions, which tended to operate on the principle of "do ut des" (I give that you might give) in which people offered worship and sacrifices to the gods in order to get favors such as rain for crops in exchange.
Many theologians see faith as a form of absolute trust in God. Although this trust is sometimes based on belief in a religious system grounded in, for example, the testimony of witnesses or cultural tradition, at other times it springs from what Schleiermacher describes as an awareness of absolute dependence.