The embeddings are used by algorithms, not people, generally. You could ask something like "what's the most similar place to X within Y", and it would using the embeddings (which cover a variety of facts) to calculate answer. An embedding is an N dimensional vector (where the dimensions may or may not be meaningful to us), and similarity can be implemented by looking at the similarity between vectors.
Yup, and while the similarity search is perhaps the most visually appealing way to work with it, the real use (in my opinion) is in providing generic sets of geospatial features which are reusable across applications. I've built out versions of H3-referenced feature sets at each of the jobs I've had over the last 10 years.