There are lots of different reasons why you might use images to accompany an idea. If you want to use data to support the idea you might include a graph. If you want to explain the idea visually you might use a diagram. But sometimes you just want to add a bit of visual flair, or convey some sentiment that comes across better visually, even if it isn't the whole point of what you're doing.
This is the basis that I use for adding drawings to my posts; the goal isn't to do the work of the writing, or to act as a more efficient delivery mechanism for information. Rather, the drawings are illustrations: they complement the text, but are totally separable. In a way, I just do two different pieces of work for one idea, and put them both in the same place. Sometimes they end up closely related, but often they're totally different and could really stand on their own.
What I'm interested in is: could you take this concept, a little standalone illustration designed to complement some main representation of an idea, and make an interactive equivalent? We use animations and interactions a lot, but they're mostly designed to be functional, like in this fairly comprehensive Google design manual. I think that's right and good as far as interactions that are the point of what you're doing. But what's so bad about pointless interaction?
Sure, nobody wants a repeat of the Flash-fueled madness of the 2000s, or the gif hell of the 1990s. I'm not advocating a return to animated starfield backgrounds or neon menus that fly around and course with faux-lightning. Instead I'm talking about small, self-contained pieces of interactivity, kind of like little windows into an interactive idea. If you want to interact with them, you can. If not, just ignore them. They don't move unless you want them to.
I think of this concept as an interactlet, a little piece of interaction. Interactlets exist in a bounded area, only respond to your input, are simple enough to understand immediately, and exist to complement some other work. Nicky Case and Vi Hart's Parable of the Polygons is an example of something close to this, but different in some important ways. The polygons are always moving, and the text is about the interactivity. It's a good post, but the interactive simulation is the point, and interactlets are for when interactivity isn't the point, but you want to add some interaction anyway.
A better example is something like the "Do Not Erase" which has been up the top of my site since forever. It's small, self-contained, simple, and doesn't get in the way of anything else. Its only problem, if you could call it that, is that it doesn't obviously ask to be interacted with. I think that's fine for its particular role; I wouldn't want it to take attention away from the content, but if I was doing one as the complement to a post I would want it to be a bit more attention-seeking.
I've put an attempt in this post, because I think it's an idea worth exploring. The main intuition to keep in mind is that an interactlet is to interactivity what an illustration is to visual art. Not the main event, just a little extra.