Can I delete all text messages in iOS 7 Messages?
iOS messages can take up a lot of space, especially if there are many videos and photos stored in iMessage and text threads. Older messages can accumulate and must be manually removed to free up storage on an iOS device.
iOS 7 has changed the process of deleting individual and multiple text messages. What if you're interested in deleting everything from the iOS 7 Messages app?
Entire message threads from a contact or group can be deleted from the Messages list. Either swipe from right to left and tap Delete, or touch Edit in the upper left corner. Using Edit provides red circles, which can be used to delete a thread.
At this time, there is no way to delete all messages from iOS 7, unless you restore your device as a new iPhone using iTunes.