You may have tried pressing Delete or Backspace or even the forward delete key to delete a conversation in Messages. If you’ve tried, you know they don’t work. What does work is to hold the Command key down while pressing Delete or Backspace (forward delete won’t work).
If you select a conversation (see below) and then press Command-Delete (or Backspace– depends on what your keyboard calls it) you’ll get a message asking whether you’re sure you want to delete the conversation.
BONUS: skip the confirmation dialog box by adding the Option key to the mix. Command-Option-Delete (or Backspace) deletes the conversation without asking whether you’re sure. So be sure!