When you suspend the computer, you send it to sleep. All of your applications and documents remain open, but the screen and other parts of the computer switch off to save power. The computer is still switched on though, and it will still be using a small amount of power. You can wake it up by pressing a key or clicking the mouse. If that doesn't work, try pressing the power button.

When you hibernate the computer, all of your applications and documents remain open (actually, they are saved to disk) and the computer completely switches off, so it doesn't use any power. It is like shutting down, but your applications and documents will still be open when you switch on the computer again.

Some computers have problems with hardware support which mean that they may not be able to suspend or hibernate properly. It is a good idea to test suspend/hibernate on your computer to see if it does work.