Proposed definition #1
Introverted Feeling (Fi) is the attitude that everything that is manifest (apparent, observable, described) is the expression of a soul or life force, in terms of which everything ultimately makes sense. Everything that happens is the result of a soul expressing its unique nature.
From this attitude, each living thing is completely unique, and has unique needs. Every living thing needs to express itself and grow in its unique way. None of this can be put into categories or measurements, at least not without blotting out that utter uniqueness of each living thing. Because we are all living things, even though each of us is unique we can still connect to the life force as it exists in others. From an Fi standpoint, the way to respond to things is in a way that is faithful to that underlying life force.
Proposed definition #2
Introverted Feeling (Fi) is the attitude of judging things good or bad based on how they harmonize or clash with a living being's inner essence. That inner essence or soul, and how things in the environment get along with it or conflict with it, is knowable only first-hand--ultimately, only by that soul. It is known by attending to one's own emotions in response to things. What you like is good--for you, not necessarily good for others. What you don't like is bad--for you, not necessarily bad for others. Anything outside your own soul is irrelevant to evaluating anything or choosing your course in life.