RSS feeds were very popular before the rise of social media. They are still in use, especially under proponents of a decentralized web.
When you write something new on your website, you update the RSS feed. Everyone who is 'subscribed' to your website is alerted to the new entry through their RSS reader.
The advantage of RSS is that there is no centralized middle man between you and the subscriber, beside the RSS readers which can easily be changed. You don't get alerted when someone subscribes, and there is no real way to know how many subscribers you have.