I fail to get how online services that support a “signature” make sense. I’m talking about those things that allow a user to draw something that almost looks like a real-world, hand-written signature on a screen on top of a line in a PDF. What am I missing?

We use hand-written signatures in our software for insurance contractors, so that the end customer can sign the contract. I know of no other way to do that conveniently.

So you print the signatures, and the customer signs on paper, right? If so, I have no problem with understanding that.

Nope. We create a Pdf with a signature marker. The signature service then allows the end customer to write their signature on the contractors tablet or on any smartphone. No paper involved. The signature is graphically included in the Pdf together with some signing measurements.

Interesting, this is exactly the case I’d like to understand. How does the signature prove anything, i.e. how do you ensure non-repudiation?

I don't know about the details. The service includes signing measurements. Keystroke information, date and time etc. I suspect, the service provider somehow needs to prove, that their service is trustworthy. Maybe some authority approved the service?