How can I Update my MacBook Pro to download Games on App Store?

I assume from the signature at the bottom of your post that you are asking about a MacBook Pro (laptop) rather than a Mac Pro (desktop).

What is the model year of your MacBook Pro? The model year of a MacBook Pro is available at Apple menu > About This Mac.

A mid 2010 through late 2011 MacBook Pro can be upgraded to High Sierra 10.13.6 but no later version. 

A mid 2012 through early 2013 MacBook Pro can be upgraded to Catalina 10.15.7 but no later. 

A late 2013 and mid 2014 MacBook Pro can be upgraded to the latest version of Big Sur macOS 11 but no later. 

An early 2015 through 2016 MacBook Pro can be upgraded to the latest version of Monterey macOS 12 but no later. 

A 2017 MacBook Pro can be upgraded to the current version of Ventura macOS 13. 

For all of the above, see instructions in: How to download and install macOS - Apple Support

A 2018 or later MacBook Pro can be upgraded to the current version of Sonoma macOS 14. See: How to upgrade to macOS Sonoma - Apple Support

Be aware that if you upgrade to Catalina 10.15 or later you will also need to update any non-Apple 32-bit apps. See: https://www.stclairsoft.com/Go64/

or

 https://www.macworld.com/article/232735/how-to-check-if-mac-software-is-32-or-64-bit.html