Safari was updated to Safari 7 along with the release of OS X Mavericks. Safari 7 is the default and a fast browser for Mac Mavericks. Safari 7 offers far better performance and cool features like Top Sites, Cover Flow, Reading List, etc.
Before the release of Safari 6 and OS X Mountain lion, users can download YouTube videos via Safari through Activity Window. However, this method doesn’t work any more in Mountain Lion and Mavericks. Luckily, you can download videos from YouTube with a Safari YouTube downloader extension in Mavericks.