As it is right now in iOS 7, there is no quick way to delete all of your message threads in the Messages app at the same time. They can only be deleted one by one. If you followed our guide on jailbreaking, you could add a "delete all" option, but this is no longer necessary thanks to Apple's upcoming iOS 8 update (which you can test out right now).
In the iOS 8 beta, you can delete multiple conversations faster, and even mark them as "read" so you can get rid of the Badge App Icons on your home screen. This minute, modest function is just one of those things that makes organizing messages... more