Below is my amateur understanding. If this was wrong please point it out to me so that I learn!
To me it looks like the concept of resolution would be a good analogy.
Let’s say a certain edge is jagged and has serrations(teeth, in simpler terms). However, the size of the serrations are different, some large and some small.
You might be tasked with counting the number of serrations.
Taking a picture of that edge at a low resolution, we would be able to make out easily the large serrations but fail to count the small ones, or even to realize that small ones exist. Taking a picture at high resolution, we would be able to see that there are actually small serration that we had previously not noticed and add that to the count, and then we can increase the resolution to see if we can find yet more smaller serrations until we feel like it is no longer necessary to look for even smaller ones.
We can think of the number of bins of the histogram as its resolution. But what exactly is the resolution of a KDE, where are the bins?
A related term to differential is infinitesimal, portmanteau of “infinitely small”. The KDE tries to estimate what it thinks the histogram would look like if the bins of the histogram was of infinitely small width, which means how the histogram would look like at infinite resolution.
This is why use KDE as opposed to just histogram with many bins as to make it fine. It doesn’t just make the number of bins high but shows you how it looks like when we approach infinity of the number of bins.
TLDR
It will allow us to identify even minute bumps and peaks and valleys in the outline of the univariate dataset’s distribution, as if the resolution was infinite.
Additional Recommended Research:
To see how “infinite bins” is really a thing that calculus does, try reading about Simpson’s Rule and Trapezoidal Rule for estimating area under a curve, which involves placing a finite number of bins under the curve in the given interval. And then integral calculus comes along and does what Simpson’s Rule and Trapezoidal Rule does but with infinite number of bins.
histogram is to Simpson’s Rule as KDE is to Integration