I find these hands-on examples of hypergraphs quite informative [0][1]. The first one for intuiting some mathematical foundations and the second one for encoding a 'time' dimension in a flat plane (althought not strictly speaking a hyper graph).

A hypergraph example of Les Miserables provided a good demonstration the d3-hypergraph package as well, but unfortunately the bl.ocks.org live examples aren't up anymore [2].

[0]: https://observablehq.com/@toja/hypercube-graphs

[1]: https://observablehq.com/@mootari/force-graph-trails

[2]: https://gist.github.com/AndreaSimeone/1e9ed38b46b95b7848c714...