You're in the middle of reading an interesting article. But what's this? Something's wrong with one of the examples! Either it's incorrect in some factual particular, or there's something the original writer obviously didn't consider, or perhaps it's just not a good idea to have it on the page at all. So you click the edit button, and write underneath, "Actually, the way it should be is..."
Wait a minute. If there's a change to be made, you should be making a change. And if there's discussion to be done... shouldn't that go on the discussion page? This is especially bad to do in a "This X has examples of:" list, as it ruins the readability of the list. If not kept in check, this can lead to entries becoming more like forum threads. And if that's the case, shouldn't you Take It to the Forums instead?
This kind of thing is also informally referred to as "natter". Mind you, this is okay in supplements that are made for it, like Headscratchers pages. It's just not okay in our actual articles. See About Rhetorical Questions for info on one of the causes of conversation in the main page. Another frequent cause is the use of YMMV items — this is one of the big reasons why we keep them separated on the YMMV pages.
A strong sign that you're indulging in Natter would be if your edits contain Word Cruft ("actually", "what really happened was"), or anything involving "I" or This Troper. Another sign is that you're adding a third-level (or deeper) bullet to an existing example. See also Signal-to-Noise Train Wreck.
Natter doesn't always have to be in extra paragraphs. See Parabombing for another form it takes.
If you come across natter, either move it to the discussion page or just delete it. Ask for help here if you don't feel like doing this. Your help cleaning up the mess will be appreciated. Also, there's a function in the page history entries which lets you send a message based on this one to the offending troper; in this case, "natter" is the message to use.
Some tropers have something to add here.