If you're going to use an external hard drive to backup what's on your iMac there is no need to partition it. Partitioning a drive is the process of dividing a drive into more than one volume. (The hard drive will actually look like more than one drive to the system.) Here's a better explanation:
Disk partitioning - Wikipedia, the free encyclopedia
Backing up your iMac hard drive is highly recommended and since Time Machine is included free with the operating system, you should use it. Buy an external hard drive that is at least as large as your iMac drive, preferably a bit larger, and use the USB or Firewire connection to attach it. Some external hard drives have both USB and Firewire, some don't. USB only will work OK.
Be sure to read up on Time Machine - how to use it, and also how to prepare your new drive for use with Time Machine.
Walkthrough: Time Machine for OS X 10.5 Leopard - Simple Help
Regards.