Time Machine requires an external drive. Open System Preferences > Time Machine. You can view if it's turned on. I highly suggest you have both a Time Machine and a clone backup.
A LOT of stuff gets included in "System." Notes, reminders, map caches, browser caches and history, SMS, MMS and iMessages, fonts and more all get included in "System." The storage graphic is often wrong. It uses the Spotlight index and when that index gets corrupted the readings are all wrong.
Use Disk Utility to find free space or do a Get Info on your Macintosh HD to find available space.
- Restart in Safe boot mode to clear caches then restart normally.
- Reset Spotlight.
Reset Spotlight in Terminal:
Enter each command followed by <return>
sudo mdutil -a -i off
sudo rm -rf /.Spotlight*
sudo mdutil -a -i on
Depending on the size of your data, this could take some time.
Follow these steps to start up into safe mode.
1. Start or restart your Mac.
2. Immediately after you hear the startup sound, press and hold the Shift key.
3. Release the Shift key when you see the Apple logo appear on the screen.
4. When you get to the login screen, you'll see Safe Boot in red in the top right corner. You don't have to stay in Safe Mode. It's for testing purposes and it clears out certain system caches, amongst other potentially beneficial things. You can either
a. Restart normally
b. Continue to login to test a problem.
More info: https://support.apple.com/en-us/HT201262