Or do you mean all messages in the messages app? If that's what you're looking to do, you can't delete all of them in one shot, but you can delete an entire thread at once. Just open up the messages app to the point where it lists all the threads you have, then swipe from right to left across the one you want to delete. You'll be presented with two buttons, Details and Trash. Pressing trash will delete all messages in that thread. But be mindful that this will also delete them off your phone as well.
Follow the same steps to delete an email thread in the Mail app.