What does ‘silence notifications’ mean?

The person you are texting has silenced their notifications and is sharing that status. They won't hear a notification when the text arrives. See the following Apple Support article for information on silenced notifications: Allow or silence notifications for a Focus on iPhone - Apple Support

Sorry, when I posted my response I was not aware of your previous reply. Responses frequently take several minutes after you post them before they appear; also, after I start a reply it can take me quite awhile (for example to search for the link to the Apple support article that I posted in my reply). I never intentionally post a reply when someone else has already done so -- but it happens. Sometimes there are 4 or 5 replies posted within the same 4 or 5 minute period and, while there may be some that are intentionally doing that, in most cases they are not intentional.

This means that the person you have sent a text message to has their notifications off meaning that they will only respond if they check the Message app.