Tannins are compounds of skin, pip and, if there is any, wood. In the mouth they feel like dryness, like velvet or like a rasp, according to how ripe and how raised they are.
Monastrell has them
It is a thick-skinned grape. A young wine may astringe; a 12-month wine may caress. Tannin is not a fault: it is the scaffolding that lets the bottle keep and stand up to a stew.
How to judge them
If they dry and bitter, ripeness was lacking or too much pip went in. If they fill and lengthen the finish, the wine is in its place. Cheese and protein soften them: that is why pairing is not a whim.