I would like to get my system the way I want it before I attempt to upgrade to Windows 10.
I have Norton Security Suite installed on my PC. In Norton's infinite wisdom, it started doing backups. Since I didn't have an external drive attached to my PC, it created a disk partition on my hard drive on which to do backups (that's really helpful if my HD crashes).
I don't know what you're describing.
Your screenshot shows two disks... one is your internal hard drive and the second is an external 1TB "backup" drive (Seagate). Is this a "portable" USB backup drive you bought and plugged in? Are you describing an earlier previous situation where Norton somehow created a "backup partition" on your internal hard drive and didn't tell you, and then just started taking regular automatic backups to it? Seems a bit of a stretch to imagine that.
In any case I don't see this backup partition you're speaking of. I only see the internal hard drive (with no such backup partition on it) as well as the external 1TB Seagate drive... which is what you'd want for taking backups.
I wonder if that Seagate external drive came with its own backup software, which you actually installed but didn't realize it? I'm not a Norton user but I didn't know it provided backup software. In contrast I just bought a WD MyPassport 1TB external USB drive for a friend and it actually did come with WD backup software on it, available for installation. I didn't install the software because I use different backup software (Macrium Reflect for "system image" backups, and NovaBACKUP for "data" folder/file backups). I only bought the WD drive as the target for the backups, but had no intention of using the WD-provided backup software.
As far as the external drive showing "active", well that's not really harmful although it might confuse you. The "active" partition on your internal hard drive is where Boot Manager lives, and is the partition where the BIOS will go to start the boot process. Since your internal drive is no doubt shown first in BIOS boot sequence (in order to locate the "active" partition where it is assumed Boot Manager lives) the fact that your external drive also shows an "active" partition isn't going to do any harm. The BIOS will discover the "active" partition and Boot Manager on the first drive in the boot sequence list, and all will be just fine.
I found out how to turn backups off, and now would like to get rid of that partition. How do I do that?
I still don't know what partition you're talking about. The "recovery" partition on the internal drive is no doubt provided by your hardware vendor when you bought the machine, in order to use "recovery media" (e.g. bootable CD or USB) to restore the original Win7 OS to "factory" state if you should ever want to or need to.
Interestingly, that "recovery" partition (which is 12GB, much larger than the standard "system reserved" of 100MB which is normally the "active" partition) is marked "active", so Boot Manager must live there along with the rest of whatever the manufacturer provided to do a complete "factory reset". 12GB is insufficient for use as a real ongoing "backup" target partition. It is about standard size for the "factory reset" recovery... not for regular normal periodic backups. That's what your external 1TB drive is for.
So, just to really be sure we understand your objective... are you wanting to wipe everything out and just install Win10 from scratch and start all over? Do you want to install Win10 as a second bootable OS on your current Win7 system? Do you have real valuable irreplaceable DATA that you must preserve, and reinstall into your newly created Win10 environment?
I don't see this so-called Norton backup partition you complain about.