There are 3 ways you can resort to remove messages. You can choose a simple way to do that.
The first method as to how to erase messages from iPhone I am talking about here is by making use of iPhone's system Settings app.
Follow these simple steps to erase messages from iPhone at once.
1. Click on "Settings" on the iPhone's homepage > Scroll down to "Messages" and click it.
2. Under "Messages" panel, scroll down to "Message History" and click on "Keep Messages" beneath to enter a new panel where you can see three options: 30 Days, 1 Year, and Forever. If you select 30 Days, messages older than 30 days will be deleted. Message older than one year will be deleted once 1 Year is selected while nothing will be deleted if Forever is chosen. The quickest way to erase messages from iPhone is to select all older than 30 days, or all messages older than a year.
3. Confirm that you want to completely erase text messages from iPhone by clicking the "Delete" button. This won't erase all messages, but it will substantially save you storage space.
4. I selected to Keep Messages for just 30 days, and reduced the storage space taken up by Messages to just 112MB! If you are running out of storage or iCloud space on your iPhone or iPad, give this a try. It is really a good way to erase messages from iPhone.
For more details of other methods, check: How to Erase Messages on iPhone?