After a few days, I decided that it was actually an annoying feature, so I clicked on Plugins to see if it could be turned off. I then noticed that I had a lot of out of date plugins. So I updated a few of them. At that point I noticed the number in the orange box had gone down. Finally the penny dropped: the orange bubble was showing me the number of out of date plugins I had. Now that really is a useful feature.
It brought home to me though the importance of reading release notes. If I’d done so, I’d have known what it was for. However I do not accept all the blame hereand feel the WordPress site designers share it with me. The reason is that if you visit the release page, you’ll see a big orange download release button, but there are no release notes. The latter is actually buried inside a post relating to the latest release inside the release RSS feed. They are actually really good release notes that include a short video detailing the new features. It’s a shame they are so buried, but now I’ve found them, I’ll be reading any future ones before installing the update.