What does it mean when the Kee Firefox extension toolbar button changes to having a yellow background?
It doesn’t seem to be related to the page(s) I’m looking at. Indeed, once it turns yellow it’s like that on all tabs.
The button reverts to normal on clicking on it, and I’m not having any problems with Kee, or any other symptoms; everything works fine. I’m just curious as to why it occasionally turns yellow…
It means you’re not logged in to the kee web page in another window.
I use the extension just locally, with KeePass. I don’t log into any Kee web page. So thanks for the reply, but that can’t be it. 
It means Kee can save a new password or has a notification to show you. You can see the notification it by clicking on the icon. If the reason is that a form has been submitted and you can save the password to a new entry, the + (add) button will briefly animate when the Kee popup opens.
I can’t remember all the different reasons it needs to show something but some of them are messages that might become irrelevant since they were created, so if you click the icon and don’t see anything of note, it’s nothing to worry about and you can just ignore it.