There are two different kinds of things that can be called "personal clouds", which could be where the confusion is coming from. If the advertisement is for a service, it's something like Google Drive, although the implementation details may differ. If the advertisement is for a device, it's just a NAS (Network-Attached Storage--that is, a hard drive that can be accessed remotely over a local network or the Internet) that's being marketed with terms that are currently trendy.
You have more control over a NAS than you would over a remote storage service, but the downside is that you're responsible for setting it up (including settings to make it accessible through your router/modem) and keeping it maintained. And they do require maintenance--my bet is that a fair fraction of those currently on the market suffer from the Heartbleed bug. Also, since a NAS is typically located in the same building as your computer, any gross physical disaster would take it out too.
My aging Western Digital MyWorldbook is probably similar to what you would end up getting, but I've never used its built-in remote-access features (actually, the first thing I did was jailbreak it), and so can't comment on them.
