Playing a youtube video is great if -and only if- you have the chromecast extension and only through chrome of course. Netflix and other chromecast-ready apps work very well.
https://www.google.com/chrome/devices/chromecast/apps.html

For media-casting or mirror-casting a local video you have fewer options.
http://allaboutchromecast.com/chromecast-how-to-guide/how-to-stream-local-video-to-chromecast/