Mac disk back up help

I have a macOS Sierra. I recently re installed OS X on my computer because it would not start. On the startup Disk window I see to different startup drives. Macintosh HD and then OS X Base System. When I restart with the Macintosh HD drive I get a message that says macOS can’t repair the disk “OS X Base system”. You can still open or copy files the disk. Back up the disk and reformat it as soon as you can. How do I get help on doing this??

Stick around for any other answers, as someone may have direct experience with this problem, but I’ll tell you what I would do if I got this error. I do have experience recovering MacOS, just not that particular error.
First thing is follow the advice given. Hopefully you backup regularly. Or, maybe you use iCloud, including Desktop and Documents.
If you feel comfortable your files are backed up, boot into online Recovery Mode (hold down Control, Option, and R as you power up), which will bring up the Mac Utilities Window. From there, you can use the Disk Utility to format MacintoshHD, and then reinstall the OS. I highly recommend you get access to another internet capable device so you can google the steps required to use Disk Utility, and online Recovery Mode.
If you do not have backups, things get sticky. You need a way to backup your important stuff. And this requires a second computer and cables to connect the two computers, or taking the disk out of the computer, or taking it to someone capable of doing it for you.
To do it yourself without taking apart the computer, the Mac provides what is called Target Mode. That basically turns your Mac into a big expensive hard drive you can copy from (hopefully). You have to have a second computer and the cables to connect the two together to do it. The cable you need depends on the model Mac computer you have.
Hope that gives you some ideas of where to go from here.

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Oh! Thank you. This sounds kind of complicated. For now I will backup all my files to a flash drive. Thank you so very much!!

This IS the recovery partition. You didn’t say where you “see” the different StartUp Drives. If it’s in Disk Utility, this is to be expected. Also:

  • Is it possible you are booting into the Recovery Mode (using that partition)?
  • Are you sure you reinstalled the OS completely?

If possible, from Recovery, I would back up my main data files before proceeding. Otherwise, I agree with what Bgeeoz said.