If you use Vimeo for sharing audiovisual contant, you may be interested in a way in which Vimeo (that, as opposed to YouTube, focuses mainly on copyright work and artwork, and offers a better compression quality and specific functions) mediates privacy for its users. Because you can share videos from Vimeo for example protected by password, avalible only through a specific link, or to allow its sharing just on choosed websites.
And this is also why, when you put an external video from Vimeo to your gallery or blog post, it may not work. Reasons for this can be several, but they are all linked to the Vimeo privacy settings.
You can set the privacy of your videos by clicking on Settings in the profile of your video, and then choosing the Privacy bookmark. There, Vimeo will show you a list of options for how you can deal with the privacy of your videos.