The user gets his or her own Web server but is not allowed full control over it (user is denied root access for Linux/administrator access for Windows); however, they are allowed to manage their data via FTP or other remote management tools. The user is disallowed full control so that the provider can guarantee quality of service by not allowing the user to modify the server or potentially create configuration problems. The user typically does not own the server. The server is leased to the client.
And while the free hosts we recommend guarantee you can keep your free hosting as long as you’d like, you will want to take advantage of additional (paid) features as your site grows. Those same providers offer paid plans to upgrade your service, however, serious site owners should strongly consider opting for a reputable, affordable, full-featured hosting provider.