I do not have this book, so I cannot know what the phrase "to relative an oracle" is supposed to mean, but I can explain the relativity of models in mathematics that results from this theorem.
In a given universe U of set theory, consider a theory T and an infinite model M of T.
According to that theorem, the cardinal of M may be any infinite cardinal (countable or uncountable, as viewed by U).
Now let us change the viewpoint, and consider the universe U with the system M inside it, from the outside : U is just a model of set theory among others.
If U is a countable model of set theory, then M will be countable too when viewed from outside U, even if it was uncountable when viewed by U.
Set theory also admits models U where the set N of natural numbers it contains, is uncountably infinite (when viewed from outside). In this case M will also be uncountable when viewed from outside (as it contains a copy of this uncountable N), even if it is countable when viewed by U.
I also wrote a site on the foundations of mathematics, that contains these issues.