The definition is just saying that "<=" is reflexive. When it says it's "a homogeneous relation on a set P that is reflexive, antisymmetric, and transitive," the meaning of P being a set is that it's an object described by set theory, and sets come with a reflexive, symmetric, and transitive equality relation -- the "native" one that comes from the underlying logical theory. (ZFC is built on a first-order logical theory with two relations: = and ∈.)