Phenomenology begins with a discipline rather than a doctrine, and that discipline is what Edmund Husserl called the epoche, or bracketing. Rather than asking whether the tree in front of you really exists outside your mind, the phenomenologist sets that question aside on purpose and asks instead how the tree is actually given to consciousness, in what Husserl called its intentional structure, consciousness always being consciousness of something. Practiced carefully, the method describes far more than trees. It can describe how time itself is experienced as a flowing present trailing a retained past and an anticipated future, how another person is experienced as a subject rather than an object, and how a religious experience of the sacred presents itself to the one who has it, independent of whether that presentation is later judged true.
That last application carried phenomenology into religious thought directly. Martin Heidegger redirected the method from consciousness toward the structure of existence itself, asking what it means for a being to exist at all rather than merely to be an object among others, and that redirection is the direct bridge into existentialism. Separately, twentieth century Catholic philosophy adopted phenomenological description as a way to talk about the human person and moral experience with precision, without first settling every metaphysical question a scholastic argument would have opened. Karol Wojtyla, later Pope John Paul II, wrote his major philosophical work in exactly this vein, describing the acting person phenomenologically before asking what that description implies theologically. Bracketing the question of God turned out to be one of the more effective ways yet found of eventually returning to it.