Imagine a virus spreads between individuals when they are in the same room. Then, consider the hypergraph where each hyperedge is the set of individuals who happened to be together in a same room. It may represent the network on which the virus spreads, doesn't it?
More generally, since hypergraphs are equivalent to bipartite graphs, they model many real-world situations.
Another example is the co-authoring hypergraph, in which each paper leads to an hyperedge between its authors.
In recommender systems, one also considers hypergraphs over products, where hyperedges are sets of products bought by a same client.
I hope this helps, good luck with your course!