Another thing to note is that this trick works with any online video streaming service and not just youtube.
Its 4 easy steps.
1) Go to www.youtube.com on your favorite browser and search for the video you want to download.
2) Play it. Let the movie buffer to end. Don't close the page
3) Open your home folder and type "/tmp" in the address bar. You see a file of prefix "Flash".
4) Copy the file to somewhere and rename it. Now you can close your browser. It is in .flv format. Now you can use a converter to convert it.
What actually happens -
All the videos are stored on youtube server. When you click play, the video cannot be played on the server. It has to be played on your machine and hence your browser instead of playing on the server, copies the file from youtube server on to your machine(computer). It stores it in /tmp directory. /tmp directory is a temporary directory. Contents of it are deleted when they are no longer of any use. That is why I told you to keep the browser on until you copy the movie file. So the browser is not actually playing the video from server, but from your local hard disk.
It shouldn't surprise you if I say that same thing happens on Windows. Video will be downloaded somewhere in temp folder from where the browser plays it. But there are some security schemes that don't let you find the file easily. Google about it to know how to do it on windows.
So, by now you might have ascertained that you can download any video and not just youtube video.