A producer tag is like a special signature that a music producer puts in their song. Just like when you draw a picture and sign your name at the bottom.
When a producer makes music, they want people to recognize their work and know that they made that particular song. So, they create a short phrase or sound that they add to the beginning or end of the track which helps people identify the producer behind the beat.
So, if you ever hear a song that starts with something like "Mustard on the beat, ho!" or "Metro Boomin want some more, nigga", that's a producer tag. It's like their way of telling you, "Hey, I made this song!"