You still see everything, just like you normally do on the forum.
The only exceptions are that you do not get a personal “reply” notice or an “at” notice up by your username icon in the upper right-hand corner of your screen. You won’t see either of these kinds of acknowledgments, if they personally reply to one of your posts/comments or to something else that you’ve said.
Otherwise, you’ll still see their posts and comments on the forum.
“Mute” doesn’t work like the “ignore” function that we had on the old forum, where you wouldn’t see anything except the person’s name, indicating that they had posted something if you had someone on ignore.