Supplementary: The prompt to do the emergency root login during boot is shown after another failure makes it unlikely the server will complete the boot process without administrator intervention. Logging in will give you a shell with enough permissions to fix most such problems. Pressing Ctrl+D (End of file key on Linux/Unix, equivalent to Ctrl+Z on Windows/DOS) will make the system TRY to continue, to the extent possible.
The program that displays the message is a special login program for such failure situations, it is specifically designed to allow a root login even without the services that normally handle logins. For example, it is used when the first operating system disk needs an fsck (equivalent to a Windows chkdsk) before access to the rest of the operating system software is available. But this is only one situation, hence the need to read error messages already on screen or stored in the in-memory boot logs.