This term is usually associated with the Danish writer Kierkegaard (although, see this link which asserts that Kierkegaard actually used the phrase "leap to faith"). The phrase seems to be used when facing the decision of whether to accept the Christian proclamation in the first place. I will use it today to refer to the decisions that people already Christian must take in the course of life.
Yesterday, I spent about two hours with a seminarian friend back from and headed back shortly to Italy. Although quite younger than I am and although I think that, in our analysis of what the future of the Church will be like, we do not see eye to eye, I did take the time to ask him for and jot down the spiritual insights or wisdom he has gained in his seminary "baptism by fire." As a young person who had to make a big decision to go off to the seminary, he came back with this phrase: "Jump and God will catch you" (he cautioned that he did not mean jumping off a building--recall here the Gospel scene where Jesus refuses to tempt God by jumping from the Temple in Jerusalem as someone slyly suggested to him).
What he meant was that we have to put our toes and feet in the water before we can tell if the water is for us. In my biblical mindset, we have to step into the Jordan before the waters part and we can enter the Promised Land as the Hebrew priests bearing the Ark of the Covenant did in the Old Testament. Step forward and see if the door opens. Step forward and see if the toll gate lifts. If the door does not open, then you have your discernment: find another path. If the door does open, then you may very well be on to something that will take you home, subject to further confirmations. Discernment does not mean waiting for a detailed map to appear beforehand. Discernment means trust, prayer, and stepping forward. Then stopping, trusting more, praying more, and taking another step. Abraham the father of faith is the model as he stepped into the unknown with amazing trust. St. Ignatius Loyola puts it in very characteristically practical, direct Hispanic terms: be aware, understand, act.
The other comment made by my young friend was to the effect that if we do discover that we have made a mistake, then we trust that God will fix it, especially if we made the mistake in good faith seeking to follow His will. Trust casts out fear. We, of all people, we who claim to be Christians would do well to stop being fearful about our next step. Otherwise, what do we have to offer to a very anxious and insecure age?
This entire issue of discernment, of course, raises the matter of the charism of discernment which is plainly taught by St. Paul as the discernment of spirits. Discernment of our next step in life is necessarily related to the discernment of spirits: which spirit is motivating and directing my next step in life? Is it my own unrealistic imagination or the spirit of darkness or the Holy Spirit? This practical reality is why we should all humbly seek the charism of discernment of spirits. We seek this charism as we do all the other charisms, not out of some sort of pride or love of the sensational, but for one very practical reason: we can't handle the task based on our natural abilities and talents alone. In spite of the strange arguments we hear that we should not seek the charisms because such seeking violates humility, it is in fact and precisely a very realistic humility that compels us in the first place to seek the charism of discernment of spirits and the other charisms also because we know that we are in woeful need of great help.