It's a 4-dimensional object. The animation doesn't show the object moving, it just shows progressive cross-sections of the object. If you stop the animation, you can choose which layer of the object to view with the slider.
Already mentioned in the comments. But still. Looks nice, but it is hard to get any insight from it. For instance, I zeroed out all weights and outputs, then slightly increased one weight. First there seems to be some non-zero bias on the minimal weight, second there is some mon-linearity which goes against intuition. It would be nice to be more clear about what is going on and then it can be more useful not only nice.
This is pretty cool. It seems impossible to mouse away while maintaining the orientation. I want to be able to perturb the weights and watch from different angles. Very cool though, nonetheless.