Your iPhone allows you to delete individual text messages, which could be handy if you need to remove sensitive information or if you want to keep your picture and video messages from eating up all of your storage space. But since it’s an infrequently used feature, Apple has it hidden in a menu.
To delete a message, tap and hold on the message until a menu pops up. Tap “More…”. Tick the checkmark next to each message you want to delete, then tap the trash can.
Note that deletions do not sync across devices, so if you use iMessages on your Mac or on your iPad, you may want to delete them on those devices as well. On the Mac it’s as simple as clicking a message and pressing the “Delete” key.