Vitamin E is an antioxidant, interfering with the chemistry of oxygen interacting with other chemicals.
Both human bodies and food are degraded by oxidation, so the same chemistry that helps protect humans can protect foods.
Vitamin E is a broad term for a member of a group of chemicals called tocopherols, which have vitamin E activity in the human body.
Synthetic antioxidants like BHT (butylated hydroxytoluene) and BHA (butylated hydroxyanisole) are chemically related to tocopherols.
Vitamin E used as a preservative is not used in therapeutic amounts, however, and the kind people take as a vitamin is itself protected against contact with oxygen until it is consumed.