Answer:
"Run Levels" in Linux are different startup or shutdown settings that can be used at any time to force Linux into a given state using the "init" command.
Level 0 forces a total system shutdown.
Level 1 switches to "maintanance mode" and only allows the system administrator to log in. This is about the same as Windows "safe mode with command prompt".
Levels 2 and 5 can be defined differently, depending on what version of Linux you are using. Typically, one of these is set to start the graphical user interface, another to start only the command line, and so on. The exact results, again, always depends on what version of Linux is used.
Level 6 forces the system to reboot.