Much like a cup of tea that’s been stewing for too long, a wine with high tannins will leave that coating.
This is also known as “the finish”. If the flavours linger long after you’ve swallowed, that’s a sign of a good quality wine. When tasting red wine, you’ll get a good idea of the tannins in the wine by how dry and astringent your mouth feels afterwards. Much like a cup of tea that’s been stewing for too long, a wine with high tannins will leave that coating.