When you block someone they will no longer be able to do things such as tag you or see things you post on your Timeline. If you're friends, blocking will also unfriend them.
iPhone and iPad:
Open a conversation with the person you want to block
Tap their name at the top of the conversation
Scroll down and tap Block
Tap next to Block Messages
Android:
Open the conversation with the person you want to block
Tap
, scroll down, and then tap BlockTap Block all messages
How do I unblock someone in Messenger?