What does unfortunately the process com.Google.process.gapps has stopped mean, it constantly appears while using tablet

FIXED ! Well almost... This problem is happening with the 'old' Android devices; Software if changing every day and most of the updates are barely tested on all devices and Android versions. The spyware, malaware, adware, are then becoming day after day more aggresive and sophisticated. So, the clean solution if format/clean/reinstall Original software, no updates.
Another helpful hint is clean all software cache, saved data, for each application , one by one, and then...
install Avast antivirus free and block behaviours, "APP LOCKING" option, at least of "Play Store" and "Downloads".
You won't see anymore the annoying message, and device will work like a charm.
Thank you, Bye. FIXED !

Go to Settings, from your pull down notifications bar or in the app drawer. Find and tap on Application Manager,(Apps or Applications, if different on your specific device). When you land in the Applications Manager, swipe right to left to get to All Applications and then look for Download Manager and tap it to open (this is the app with the Android as a logo). Press disable, then enable it once again. Hope this helps!

This is related to a recently installed application causing a conflict or you may need to clear the application cache.

Here is a great article and some screenshots to guide you.

http://www.androidpit.com/process-com-google-process-gapps-has-stopped-fix