If you have a slow Internet connection or if you frequently watch some videos, the new feature allows you to cache the videos, close the browser and watch the videos at a later time. You may want to increase the size of your browser's cache to preload longer videos. Here are YouTube's recommendations for dial-up connections:
"For best results, you may want to start the video player and then click on the PAUSE button immediately. Then, wait until the red progress bar has reached the end of the video before playing it. Allowing the entire video buffer lets you watch it without interruption."
Videos will load from the browser's cache even if they're embedded in a web page, so this feature is not limited to YouTube's site.