There are many points of view on this. Jung's original e/i distinction involved a distinction that closely resembled what in the Myers-Briggs dichotomies is ES/IN -- the latter were described as oriented more to the inner life, the former more to the external world, were more social, worldly, less meditative, and so on.
Of course, beyond these descriptors, Jung also had a model of the psyche, where the inner life meant the collective unconscious, a repository of potential for experience consisting of "raw material" called archetypes, which manifest in different ways in different situations.
So to him, the introverted feeling function attempted to pursue value judgment against an inner ideal that is glimpsed against the collective unconscious. Archetypes could be compared to platonic forms or whatever.
The Myers-Briggs system has non-dichotomies functions-oriented content as well, and in it, the major change is that a lot of Jung's e/i stuff is now in S/N, and thus, e/i in their system is less about outer vs mind and more in my experience about personal vs collective. Hence, Fe is viewed as pursuing more collective ideals in value judgment, whereas Fi is viewed as a highly personal value judgment system. One seeks harmony with external conditions, and one harmony with inner conditions. Ti is defined similarly -- one's personal logical framework, vs Te which seeks external standards for consensus, such as efficiency or whatever.
The actual motivation behind this is that in the dichotomies, J/P is what decides your use of Ji vs Je, and this is I think ultimately rooted in the fact that J correlates with Big 5 Conscientiousness. Myers didn't necessarily know about the Big 5 or anything, it's just that J's content is similar to Conscientiousness content, and you can imagine Conscientious types are more likely to seek firm external criteria we can agree upon as the standards/protocol, vs P types care less for this, so Myers tried to frame this as if P types seek a more internally consistent than externally consistent framework for judgment.
My own preferred version of things prefers socionics' take on e/i (note I dislike a LOT of socionics things, and my actual views synthesize aspects I like -- some socionics, some Jung, some other thinkers outside of typology, and my own thinking), which says e/i is about objects vs relations.
The most primitive example of this says that objects~the sensory world, relations ~ the logical world, where we impose logical relations (including causality) on a world of objects where ultimately there simply exist sequences of events with no relations...where even our perception of sequences is our imposing time-relations on a world that may not contain them.
So in this framework, the gist is Ti is structural logic, and Te the factual-algorithmic logic, Fe the ethics of emotion and Fi the ethics of relations. The Ji's are more responsible for defining the framework within which you operate, so where Fe ensures you have an appropriate feeling-toned/valuative response to objects, Fi defines the ways you relate to things -- obviously one cannot exist without the other.
Similarly, one cannot produce logical facts without some kind of framework in which to talk coherently of things, but one can psychologically emphasize the refining of such a framework or one can be more organic about that and more interested in letting the kinds of factual outcomes produced dictate.
Anyway, an example of this latter version of Fi would be when someone is said to ethically relate to things based on their culture, or their species. This would e.g. emphasize compassion less as a property of whatever object evoked it, but more as a property of the way we as a human species are inherently built to relate to ethical situations. Just as Ti might define the axiomatic framework one is bound to in order to talk coherent of a topic, Fi similarly reminds us what our ethical framework is. Any emotional arousal that is felt betrays an ethical framework, because it contains feeling-toned and thus pre-evaluative content, in this school of thinking.
My view is: choose whatever version of Fi you like!! I have a framework in which I type as ILE (NeTi), and I chose it after I carefully considered what seems to me to be the ideal organization of all the ideas.