If you joined Vimeo via Facebook, you will need to set a password for your Vimeo account before performing any actions on the site that require a Vimeo password, such as deleting videos, deleting your account, or signing in from different devices.
This step is required to ensure that you'll be able to maintain access to your Vimeo account separately from Facebook in the future. Once you set a password, you won't need to be logged in to Facebook in order to use any Vimeo feature.
To set a password, go to your account settings, then click Password on the left sidebar. Once there, click on the Change Password link. There, you will be prompted to enter in a new password and confirm that new password.