I never understood signatures, but then my handwriting is all over the place and at best my signature is a squiggle.
I haven't a clue how they're verified these days. I suspect they're basically a legal guarantee, where in court you can be asked "is this your signature".
Signatures are basically the same as credit card numbers. Not secure, but everyone keeps pretending they are, so insurance and legal make sure they are.
We can "sign" something by entering our name into a text box on a web form. That's the easiest to reproduce. This works because the contract is between the other party (requestor) and the named person. Entry by any other party not authorized by the signer will render the contract null and void.
The signature answers the question of, "Does X agree to these terms or not?" and not, "Is X who they say they are?"
Depends on the country. In Czechia, some documents (such as the contract about selling/buying property) require verified signatures, where you go to a notary or a post office with your ID card, sign the document in front of them, they note what document you brought to them into a book of signature verifications and stamp the document.
Mail-in voting in my state entails "signature verification", wherein I learned - the hard way - that they do in fact compare the signature on my ballot to some signature they've got stored somewhere to see if it matches.
I haven't a clue how they're verified these days. I suspect they're basically a legal guarantee, where in court you can be asked "is this your signature".
Digital records are IMO better.