This is a great description by Chris of the problems that webmentions aim to solve.
If you use Twitter, your friend Alice only uses Facebook, your friend Bob only uses his blog on WordPress, and your pal Chuck is over on Medium, it’s impossible for any one of you to @mention another. You’re all on different and competing platforms, none of which interoperate to send these mentions or notifications of them. The only way to communicate in this way is if you all join the same social media platforms, resulting in the average person being signed up to multiple services just to stay in touch with all their friends and acquaintances.
Given the issues of privacy and identity protection, different use cases, the burden of additional usernames and passwords, and the time involved, many people don’t want to do this. Possibly worst of all, your personal identity on the internet can end up fragmented like a Horcrux across multiple websites over which you have little, if any, control.