This advice was given to young Luke Skywalker by Obi-Wan Kenobi in the first Star Wars movie, A New Hope. It is a question to wonder why this advice needed to be given to Luke in the setting of the movie and to us as movie-watchers in second half of the 20th century. The advice given suggests that we might otherwise trust some other of our faculties, presumably our minds, for guidance. Humanity has trusted and relied upon the mind and its products off and on for centuries, attempting to conquer or ignore our 'baser' selves -- our passions, lusts and desires. In medieval scholasticim, rationality and rationalism powerfully informed and affected medieval theology, particularly in natural theology, in which certain self-evident or 'common notions' were said to lead to, or perhaps even prove, the existence of God and something of his attributes. One of the significant contributions of post-Reformation thinking was the realization that the mind was not immune to the effects of our fallenness. If our desires and emotions were affected by the fall, then so equally was our thinking. We could not reason our way infallibly to saving truths, although we could infer some general truths from general revelation, albeit fallibly. No, our passions and thoughts, the whole person, were in need of redemption, and both needed to be sanctified and redeemed by the power of Christ in us. Thus, reason was subordinated to divine revelation in the Scriptures; our thoughts were to be brought 'captive' to Christ, redeemed, recalibrated and reset for a true knowledge of the sacred and also a re-framed knowledge of the natural, physical realm.
With the Enlightenment, the mind was 'freed' from the shackles of subordination to the Scriptures and could proceed on its merry way without such restraint. Natural theology was replaced by the immense explanatory power of science. As the Enlightenment progressed into modernity, science and rationality was the rising and unchallenged king, for a time. Then the incompleteness and moral vacuity of science began to take its toll, as we discovered that being treated and understood as purely physical beings operating purely in the physical realm was hollow. The immense gains and progress from science and technology were indisputable, but critically insufficient.
Into this context in the second half of the 20th century, George Lucas introduces the characters and setting of Star Wars. The mind, having been elevated higher than its proper place, had failed to bear the weight placed upon it, and a return to some form of spirituality was needed. The spirituality in question was a quasi-Eastern form of religion involving 'The Force' which could be harnessed for good or evil and which had both good and evil in its essence. The Force was made available to its mediators (Jedi knights) by techniques and practices in which the mind, the rational component of us, is shut down or sidelined. Thus, the advice to Luke.
The message is to trust our feelings because we cannot trust our minds. It seeks to place the same weight on our feelings and passions that was placed on our minds and which our minds could not support. Why should we expect our feelings to do any better? Why should we trust our feelings? If our minds have failed us, it is because we placed too much weight on them and separated them from revelation, and not because our minds are inherently less capable than our feelings and passions. Our minds have the invaluable task and capability of filtering our sensory input, thoughts and even our responses by appeal to reason, based on revelation and substantiated by our experience. Why would we give this up? Our passions and feelings, apart from the contributions of rationality, are vulnerable to spiritual fraud of various kinds.
No, the answer is that all parts of us, our rationality and passions, have their place in our whole person, serving the role that God has laid out for us, but only if we bring them all, our whole selves, to God and worship him and only him. In our society and media, we are bombarded with messages like "follow your heart", "live your passions" and others like it. It is as if our hearts and passions are better indicators of what is true and good than the simple truths of Scripture communicated verbally in rational form (it must be clear, however, that the message of the Scriptures, while framed in words and discourse, is not limited to the rational realm and contains spiritual depths and dimensions). This assumption is false and deceptive. If you're reading this, turn away from that mode of thinking and living. Live life as a whole person, including both your rationality and passions. Don't throw one away and expect the other to do all the work, particularly apart from the word and spirit of God.