To writhe is to squirm and twist. Often you'll see the phrase "to writhe in agony." Writhe when you've just ingested some stomach-wrenching poison, or perhaps in response to red ant stings.
Writhe stems from the Old English, meaning "to twist or bend." It's not a coincidence that a Christmas wreath is greenery twisted and bent into a circle. A person can writhe in embarrassment but it's usually reserved for times when pain or discomfort cause you to twist and bend over and squirm because your body is in such distress.