You may have noticed while watching videos on YouTube that Google doesn't offer a 'download' option. This is likely by design, and is most likely a way to give content creators more control over what videos are out there. But in reality, streaming a video and downloading a video are very close to the same thing. In order to stream a video on YouTube, your computer still needs to 'download' the bits in order to play it back. The only difference is that you can't access that file locally, but there are third party tools out there that will make this possible.
There's a site that makes it very easy to download YouTube videos: YouTubePP.com. All you have to do is find the video you want on YouTube, then add the letters "PP" after "YouTube" in the URL, and it will take you to the page where you can download the video. Other sites that will do this include OnlineVideoConverter.com, JDownloader.com, and SaveFrom.Net.