"Closed" under a property, means the result obtained after using the property, belongs to the considered universe W.
So, closed under the axiom of infinity means you can construct an inductive set, and this set is a member of W.
Now since the universal set W you are examining need not contain numbers, the inductive set you obtain need not be the set of natural numbers.
For example, say your set contains the ordinal . Using the axiom, your universe contains all the ordinals up to