My guess is you may have signed up for two-step verification? If so, be aware that Apple made some security changes recently (thanks to the celeb photo leaks). Many third party apps now require app-specific passwords, the goal of which is so that you are not using your master iCloud password with third party apps, where security may be lower than what Apple expects.
What was confusing for me is that, unlike a couple of messages in the last 2 weeks (Mail and one other I can't remember), this particular message I started receiving today did NOT mention an "app-specific password is required". It just said my iCloud password was incorrect (and I verified that it WAS correct). BUT.... the error message had an icon:
I finally remembered it to be Fantastical, a small (and great, I might add) Calendar app.
So... you may have a third party app that, like this one, isn't being clear as to what is needed... you just need to get a third party app-specific password. Hope this helps:
Follow the steps below to generate an app-specific password:
- Go to My Apple ID.
- Select Manage your Apple ID and sign in.
- Select Password and Security.
- Click Generate an App-Specific Password and follow the steps on your screen.
After you generate your app-specific password, enter or paste it into the password field of the third party app as you would normally.