If you are signing in to your Chromebook and your password has recently changed, make sure to put in your old password when prompted. However, do not worry if you do not remember it. What you can do is simply select Forgot old password.
If you do this just know that all local data that was previously saved on your Chromebook will no longer be available, only synced data and settings will be restored.
Embedded below is a 33 second YouTube tutorial.