As you can see in "statement of the theorem" in http://en.wikipedia.org/wiki/Implicit_function_theorem" , or
perhaps a little clearer in Implicit Function Theorem -- from Wolfram MathWorld ,
this is almost the exact wording of the implicit function theorem, so I don't understand what is it
that you cannot understand here?
Perhaps it is just a matter of writing so that it'll look clearer...?