You can play YouTube videos as well as local files, although in this case both of you need to have the file on your computers. To connect with the other person, just use the automatically generated link when you get to the site.
This application also lets you save videos to Dropbox and Google Drive in order to access them quickly. You can also talk with the other person via the integrated chat, which lets you share comments on the video you are watching.
Gaze lets you feel close to the person that's watching the movie with you, letting you enjoy watching movies or TV series with company despite being hundreds of miles apart.