Vine is a latest mobile app owned by twitter, using vine you can create and post 6 seconds length video clips. Present Vine is available for iOS and Android, Windows Phone version coming later this year. You can view Vine videos shared from iOS or Android phone on your desktop browser.
You can easily download any Vine video from your browser. Just right click the video and then select the download option and save the video onto your desktop.
Here is the video tutorial to download Vine videos to desktop.