Twitter unfortunately does not offer any kind of way to delete all your tweets with one click. You can go through and delete them one by one but if you have over a thousand tweets, you're going to be there for a very long time. TwitWipe is a cool new service which enables you to delete all your tweets but keep all your followers, favourite tweets and the people you're following.
This can be a great service to business accounts who might be re-branding. They can delete all their old tweets which link to their old site but keep all their followers too. Or maybe you just want to start fresh, this is the best way to go.
Obviously you will want to think about this carefully because there is no going back.
Only if Facebook offered a service like this with their new revealing Timeline feature.
You can head over to Mashable to see the video which explains more - here.