If you're just looking to animate what the plot is doing like in the video, just include a 'drawnow' command inside a for loop.
If you want to create a movie from within MATLAB you can use the getframe and movie commands to capture the figure graphics to an animation.
You can also create a frame-by-frame animation by saving a series of PNG files and converting them to a movie with an external player (such as Quicktime) or you can write an animated GIF directly using the imwrite command. With the 'append' option for imwrite you can add multiple GIFs with a defined delay between frames. For the type of growing bar graph like in the YouTube video, an animated GIF is going to be a lot smaller than any "normal" movie file.