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. If your mac can upgrade to Sierra
it can upgrade to High Sierra which still receives security updates.
The model and year of your Mac will determine which macOS you can upgrade to,
read the following links.
How to upgrade to macOS Sierra - 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.