The App Store Updates page only informs you of updates available for the OS you are currently running.
As you are running an older system then you are probably up to date on that system.
If you want to install a newer OS that is called an Upgrade.
The model and year of your Mac will determine which macOS you can upgrade to,
read the following links.
How to upgrade to macOS Mojave - Apple Support
How to upgrade to macOS High Sierra - Apple Support
Before upgrading make a full back up of your Mac.
Check that third party apps you use have updates available for the new OS.
https://roaringapps.com
Check that your printers/ scanners etc have updated drivers and software available for the new OS.
macOS Catalina 10.15 was released recently, the latest version of macOS.
If you are considering upgrading to Catalina be warned that it does not support 32bit apps.
Your Mac is probably running 32bit apps and these will need to be updated to 64bit apps,
some updates may be free, some may be paid. Use this app to discover which apps you have
are 32bit, https://www.stclairsoft.com/Go64/. Once the list has been created you can then
contact the developers of the apps to see if they provide 64bit updates.
How to upgrade to macOS Catalina – Apple Support
If you get the error that the copy of High Sierra is damaged and can't be used to install macOS
means the App Store has detected a copy of High Sierra on your mac. Look I'm your Applications folder
for Install macOS High Sierra.app, move it to the Trash empty the Trash. Connect your mac to your
router using a cabled connection, Restart your mac and go back to the App Store to download High Sierra,
see above if you want High Sierra you might prefer Mojave or go to the stroppy youth of Catalina.
