My reading of it is that it's a database you control that you can allow third-party web applications to use. So instead of the web application storing your data

My reading of it is that it's a database you control that you can allow third-party web applications to use. So instead of the web application storing your data on their servers, they store it on yours. From the perspective of the end user it's useful because retain control over your data, so there's no barriers to switching to a competitor, for instance.