Tannins stem from four primary sources: the grape skins, seeds, stems, and the wood barrels used during aging. They provide texture and mouthfeel to wine as well as a sense of weight and structure. ... Tannins create the drying sensation in your mouth when you drink a red wine.
If you're trying to understand what this feels like, brew an incredibly strong cup of black tea and drink it. That drying sensation is caused by tannins in the tea. It's similar in wine!