OS X Yosemite

A 2103 iMac can upgrade to any of the following OS's.

Mac OS X El Capitan 10.11, macOS Sierra 10.12, macOS High Sierra 10.13, macOS Mojave 10.14, macOS Catalina 10.15

If wanting to upgrade to Mojave or Catalina upgrade to High Sierra first.

Open Safari and click on this link, 

How to get old versions of macOS – Apple Support

Go to Check Compatibility to see if your mac qualifies for the OS upgrade you want.

Then go to the Download OS section and click on the OS you want to install.

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.

Connect your mac to your router via cable rather than rely on WiFi.

Do not use your mac while it is downloading

and do not use any other devices that share the same internet connection.

If the App Store says ‘Open’ then it is detecting a previous download of the install app

go to the Applications folder locate Install macOS ******.app.

Move it to the Trash, empty the Trash.

Restart, click on the link again, the App Store should say ‘Get' or 'Download'.

If you are considering upgrading to Catalina be warned 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/ then contact the developers of the software to see

if they are offering 64bit updates.