Sleep mode means your user session is kept stored in the memory (RAM) while everything else (other than LED lights) is turned off. If you unplug your PC while in sleep mode, you lose all unsaved work since RAM is not able to store data without electricity unlike Hard drives.
Hibernate means the user session that is stored in the memory is stored in a file called hiberfil.sys and then Windows completely turns off all the devices and the computer itself. You can uplug your PC safely by using this mode. When you turn on your PC, you basically get to your previous user session.
Shutdown is self-explanatory.