Just to add my own info to the mix.
If you are like me and didn't have an external drive big enough to backup the PS3 HDD you currently use there is a very very easy solution.
Step 1:
Buy one of these (doesn't need to be this exact one mind you)
Step 2: Put the new HDD inside it and connect it to your computer
Step 3: Format it to FAT32. This can be done via the command prompt but I prefer using
this small self contained exe.
Step 4: Connect the new drive in the enclosure to your PS3 and backup the PS3 to it
Step 5: Connect the new drive back to the computer and transfer the backup to your computer. It is going to be about the same size as the total space used in your PS3. So if you have a 250GB HDD and are using like 180GB of it, then your computer needs to have 175-180GB free (for a small amount of time).
Step 6: Swap the drive in the PS3 with the new drive that is in the external (so now the new external drive is inside the PS3 and the old PS3 drive is inside the enclosure)
Step 7: Format the external (containing the old PS3 drive) to FAT32
Step 8: Transfer the backup to the external
Step 9: Restore backup to the new PS3 drive.
I know it is longer then just backup and restore, but I am unsure how many of you guys have external drives big enough and this is only $15 more to do it this way. Also when you're done you'll have an external HDD to use for whatever you want.