I have thought quite a lot about this.
Based on what I've read, from a neurological perspective, there are certain changes that occur. One is the development of a generalized motor schema (I think it's called). It is similar to what happens when you learn a sport, and you learn a new class of interrelated movements. This then makes it easier for you to learn newer movements when they relate to that.
Another is development of the understanding of structure, which allows you to keep more music in your mind at the same time, and artificially "boosts" your working memory. Essentially, what happens is that you acquire an intuitive understanding of a musical form, say, theme and variations (this is grossly oversimplified) -- then, your mind has this structure internalized, and whenever you listen to or learn a new piece of music, it is "filling in the blanks" rather than starting from scratch. This is what happens in other fields such as chess which require exceptional memory as well.
There is pretty much improvement in sound processing in general. It looks like this varies by the age at which you start out, but I have certainly felt the difference even though I started out as a late teenager. For example, I think it was demonstrated that musicians are better at distinguishing phonemes such as "pa" vs "ba", as well as at learning foreign languages. I have also clearly observed that I can now hear music more clearly, and this aids my transcription ability. For example, it took me a long time to actually be able to clearly hear bass notes in music and transcribe them accurately, which I can now do. I can also hear textures on the piano clearer and it almost feels like I can hear every single note, whereas initially, while I could hear the melody, a lot of the accompaniment felt more "smudged", and again I remember this quite clearly as I started out as a college student.
At the high end, it has been demonstrated that the pianists pretty much become ambidextrous from a mental standpoint when it comes to use of the hands for the piano -- it's almost as if the brain forgets about natural handedness when it comes to the piano.
As to what you're improving, everything really -- the ability to memorize music, the ability to perceive fine differences in sound, the ability to multitask, creating that generalized motor schema for playing the piano and the related coordinations, and so on.
From the sample of pianists that I have seen, a few things have struck out to me -- an unusual facility with language which often extends to proficiency in multiple languages as well, high working memory which manifests itself in a bunch of ways including being slightly quicker to pick up on a number of things, perfectionism,
I think there are certainly ways you can optimize how you can improve your rate of progress -- you should not settle for learning slowly by any means. Read some of the posts on here by bernhard, lostinidlewonder, etc. -- they have a lot of good ideas. Also, there are a number of Youtube channels which go into these topics.
Here's a recent discussion which was very similar:
https://www.pianostreet.com/smf/index.php?topic=67482.0