The ticks next to your messages show their status: whether a message has been sent, delivered to the other person's device, and read.
Read receipts are a setting you control. If you turn read receipts off, you won't see when others have read your messages — and in turn, they won't see when you've read theirs. You can change this any time from your privacy settings.
Turning off read receipts doesn't stop messages from being delivered as normal; it only affects whether read status is shown.
