If you block someone, you will be able to send messages to, but not receive messages from, that person.
If you are blocked by someone, you will not be able to send messages to the person who blocked you, even though you can receive messages from that person.
- Go to the Inbox and open the conversation thread you have with the contact
- Tap the contacts name or phone number at the top middle of the screen
- Scroll down and click "Block" or "Unblock"