for software (typically Web apps) offered as a service, running on someone’s server you don’t control
The tag hosted should only be used if the solution has to run on an online server that’s not under your own control. So you are the user of a service, and you don’t install the software yourself.
Typical examples are Web apps (e.g., Google Docs), but the tag can also apply to software that doesn’t necessarily have a Web interface (e.g., for file-synchronization over the Internet).
If the software should run on a server you control, use the tag self-hosted instead.