… addition.

A set is closed under addition if you can add any two numbers in the set and still have a number in the set as a result.

… (scalar) multiplication.

A set is closed under (scalar) multiplication if you can multiply any two elements, and the result is still a number in the set.

Generally, “closed under some operation” means the elements of the set are not being able to “escape” the set using that operation. The result always the set they are from.