A Set is closed under a binaryoperation if any two elements of the set when combined using the binaryoperation produce an element of the same set.
Thus a set A is closed under the binaryoperation * if for all a and b $\in\$ A then a * b $\in\$ A.
This idea extends beyond simple binaryoperations.
For example:
The set of natural numbers is closed under addition and multiplication
but not closed under subtraction.
The set of the integers is closed under addition, subtraction and multiplication
