X and Y are variables used for writing axioms about roles (such as be-child-of) in a form of If ... then ... rules or ... if-and-only-if ... rules. Those axioms are OWL expressions. The axioms include: general role inclusion, transitivity etc. The axioms modify semantic sense of the roles. All of them are in fact a kind of semantic sugar and can be thought of as special cases of a general role inclusion and concept subsumption axioms.
The examples below show how to write simple axioms about roles using variables X and Y.