YouTube has all the buttons—Upload, Browse, Subscribe etc.—, but it doesn't come with an inbuilt “Download” button. Viewers have to use third party software to download the videos from YouTube. Why is that?
Because the premiss of the site is that you go back to view your favourite videos so you can see (more) advertising, sponsored links etc.
If you download the videos you could watch them as many times as you wanted without seeing all this.
There's also the small matter of copyright - you only have the right to view the videos, not copy and (potentially) redistribute it.
I've heard some news about YouTube will update to open the download function later. You can expect that:D The downloaded file will be saved for 48 hours and then it will be delete when next time you connect the Internet...That's all I read on some news report.
I also know a very good third party software to download YouTube videos for 100% free. But it will be better you only use the downloaded videos for personal enjoying not for commercial use. (It's called iSkysoft Free Video Downloader.)
This iSkysoft company is doing especially good at Mac OS X and they also provide Windows solutions. You can search it on google, it has three ways to download videos: download button, drag and drop, and copy paste url...This is the YouTube downloader I’m using and probably the best freeware.