You cannot move program or system files. In fact, I don't think Windows will even allow it. If you have documents you've created, pictures you've stored, etc., you can copy/paste them into folders you might create on the external. I would recommend that you consider doing a Windows clean-up of the drive to remove temp files and even windows update files. You can also trim back the amount of space Windows uses for it's "system restore" feature.
Keep in mind that moving user files is not a backup method. You should still consider providing at least one more source to keep data that you consider to be important or irreplaceable.
My computer itself only has 64GB of storage, so I'm constantly getting messages of low disk space. I have a seagate external hard drive, but I don't know which files I can safely move onto it and remove from my computer. My computer has no disk space left, but when I click on the hard drive in files, all I see are these items; MSOCache, Program Files, Program Files (x86), Program Data, Users, and Windows. These all seems like necessary items to have on my internal hard drive, so how do I free up space using the external hard drive? Can any of these items be moved to it, or is it possible to download programs (like Avast Anti-Virus, Steam, etc.) onto the external hard drive and run them through only that? Help!