I played with D3 every now and then for maybe the past 6 years to scratch some data visualization itch, but I never really understood it. I always wound up trying a code snippet from a random blog and got frustrated when I couldn't get it to bend to my needs.
It finally clicked for me a after I read the first few introductory tutorials on the D3 Github wiki. It made me realize that, while it was probably built for data visualizations, D3 at its core is a browser DOM manipulation library with a (data-driven) declarative API. It's a slightly higher level of abstraction compared to the DOM manipulation part of jQuery (though, many frontend developers these days consider jQuery to be a low-level library).
Of course, it also helped that I learned a lot over 6 years. I was a university student back then, and now I'm a professional software engineer who has spent the last year or so doing frontend development. D3 makes a lot of sense within the context of my current understanding of how browser DOM APIs work.
I am disinclined by temperament to use low level tools for tasks that really should have a sensible generic abstraction. I know some people's brains err in the other direction - each to their own.
(I'm pretty sure tools exist. I used https://bokeh.pydata.org a few years ago when I needed something along these lines. I looked at d3 and had a similar reaction to the grandfather comment)
If I ever have to make a chart with another language, I cry because I can't use d3. I have reimplemented portions of d3's api in other environments like native Android before. Digging through the docs to find whatever configuration variable I'm supposed to set reminds me of the days of jquery plugins.
The d3 specific parts are the idea of mapping data to DOM elements (which is the part I think is beautiful), how it uses the data join to do so, and how you use the scale functions to map from data space to pixel space to set the element positions and other attributes.
Feel free to email me if you like -- it's on my profile.
In practice, handling dynamic updates requires so many hooks into the data that you can't really define a sensible abstraction layer and have it work well for both simple cases and complex cases. D3 is the successor to Protovis, itself the successor to Flare, itself the successor to Prefuse. And having used all of them save Flare (since I've never had the ability to write Flash code nor the desire to do so), d3 is the only one that I've actually enjoyed using.
[1]: https://nvd3.org
I was under the impression that a lot of higher level libraries were built on it.