Apple has been experiencing heavy server loads yesterday and today that caused one of the developer download checks to experience problems. The end result is the error you're getting. Everyone was getting this yesterday. Some still today. I assume you're using the standard software update: Apple > About this Mac > Software Update? Eventually you won't get this error. They're working on it (per AppleCare phone call).
If you don't want to keep trying it every few hours to see when they fix it, try just downloading the update from the App Store directly. I did that last night and it worked fine. Keep in mind:
- Always back up your computer using Time Machine to an external hard drive prior to updating the operating system. If there are problems or you lose data that's the fastest way to restore it.
- As a redundant backup you may want to also have an off-site cloud based backup (house burns down, laptop stolen etc.) like back blaze dot com
- Big Sur is a HUGE update in that it's over 12 GB in file size. It will take quite some time to download, especially when the world is also trying to download it at the same time - some users have experienced slow downloads. You can shorten that time by connecting your laptop to your router hardwired via ethernet cable, which provides for faster internet speeds than wifi does.
- Be patient. On a fast internet connection it took me over an hour to download and over 30 mins to install.
Here's the App Store link to Big Sur: https://apps.apple.com/us/app/macos-big-sur/id1526878132?mt=12
Let me know if this works for you.
Hope this helps!