What Mac and what OS are you using?

Partitioning the disk does nothing for the Mac, it is more of a Windows thing.

Backing up your "Home" folder is all you need to do.

If you have OS X 10.5.x you could use Time Machine to backup to an external drive and there are a number of other pieces of software that will backup your data.

"Backing up" your files to another partition on the same drive is NOT backing up. It is just moving your files to another place on the same drive and ALL of it will go away when the drive fails.
You HAVE to back up to an external media for a backup to be of any worth.

P