There's no information in the repo, but I suppose this means jpeg compression of an encrypted image without decryption, right?

Yes. Homomorphic encryption means that you can do math to the encrypted file to produce a new encrypted file. The operator doing the math cannot read either version, but the owner of the original file can.

Without anyone ever seeing them?

About the encrypted DB: https://people.csail.mit.edu/nickolai/papers/popa-cryptdb-tr...

All I remember is that this didn't end up becoming practical because of some limitations, which were maybe discussed in the paper. Something about leaking row counts.

There's such thing, at least in prototype stage. Like cryptDB, which, afaik is homomorphic with a nice property of preserving the order of encrypted keys. It leaks some information, but you can apply predicates different than equality, like `where a between 100 and 200`. In that case, the query passed to server will look like `where a between encrypted(100) and encrypted(200)` and server will be able to apply it, without knowing real values of the range limits or data stored in `a` column. With encryption function which don't preserve order, the data would need to be filtered client-side, so whole projection would be dumped to client and it would be the client who first decrypts the data, and then filters-out unnecessary rows.