A leap of faith, in its most commonly used meaning, is the act of believing in something without, or in spite of, available empirical evidence. It is an act commonly associated with religious belief as many religions consider faith to be an essential element of piety.
The phrase is commonly attributed to Søren Kierkegaard; however, he himself never used the term, as he referred to a leap as a leap to faith. A leap of faith according to Kierkegaard involves circularity insofar as a leap is made by faith. In his book The Concept of Anxiety he describes the core part of the leap of faith, the leap. He does this using the famous story of Adam and Eve, particularly Adam's qualitative leap into sin. Adam's leap signifies a change from one quality to another, mainly the quality of possessing no sin to the quality of possessing sin. Kierkegaard maintains that the transition from one quality to another can take place only by a "leap" (Thomte 232). When the transition happens, one moves directly from one state to the other, never possessing both qualities.
It is important to understand that Kierkegaard felt a leap of faith was necessary in accepting Christianity due to the paradoxes that exist in Christianity. In his book Philosophical Fragments, Kierkegaard delves deep into the paradoxes that Christianity presents. One of these is the belief that there existed a being (Jesus) who is both 100% man and 100% God. Since neither logic nor reason can reconcile this, one would require faith to believe it in light of the paradox. So, when one decides to have faith that a being existed as both God and man, one makes a qualitative change from non-belief to belief, and thusly makes a 'leap of faith' that it is true.
The implication of taking a leap of faith can, depending on the context, carry positive or negative connotations, as some feel it is a virtue to be able to believe in something without evidence, while others feel it is foolishness. It is a hotly contested theological and philosophical concept. For instance, the association with "blind faith" and religion is disputed by those with deistic principles that argue reason and logic, rather than revelation or tradition, should be the basis of belief in God.
Even some theistic realms of thought do not agree with the implications that this phrase carries. For instance C. S. Lewis argues against the idea that Christianity requires a "leap of faith," (as the term is most commonly understood). One of Lewis' arguments is that supernaturalism, a basic tenet of Christianity, can be logically inferred based on a teleological argument regarding the source of human reason. Nonetheless, many Christians are not too critical of the term, and do accept that religion requires a "leap of faith".
What is often missed is that Kierkegaard himself was an orthodox Scandanavian Lutheran in conflict with the liberal theological establishment of his day. His works built on one another and culminated with the orthodox Lutheran conception of a God that unconditionally accepts man, faith itself being a gift from God, and that the highest moral position is reached when a person realizes this and no longer depending upon themselves takes the leap of faith into the arms of a loving God. In a Lutheran context, the leap of faith becomes much clearer.