My understanding was that when you "muted" a conversation in Gmail, future emails came in but they didn't bring that conversation back into the inbox. I clearly don't understand how this feature works because I just muted a conversation, and archived it, and a new email came in and it shows as unread again.
You are correct. Muting a conversation archives it and any new emails that fall under the conversation (same subject) will skip the inbox and be archived.
I'm guessing you might be stuck on this next part though, as it seems to lessen the value of the feature itself.
Muting a conversation does not normally work if your email is in the
Cc field. However, there is now a feature in Gmail Labs called Smart Mute that will keep a thread archived as long as your email address was not added to the
Cc after you clicked
To expand on @Rebecca's excellent answer: This feature began life inside Google as a way to mute conversations on the panoply of internal mailing lists. If you were subscribed to
firstname.lastname@example.org, you saw every reply to every thread, but those replies were to
email@example.com, not to you. The designers didn't allow for the fact that most people outside Google will want to mute conversations that are actually CC'ed to them.