The distinction between formal and objective reality in Descartes is elucidated on Brown's web page. Formal reality refers to the reality of an object by virtue of the kind of thing it is (infinite, finite, modes/thoughts). Descartes view of formal reality is encapsulated in this online commentary:
"When Descartes speaks of things as having more or less reality than other things, we can understand him as roughly dividing up reality along a scale where infinite substances (i.e., God) have the most reality, followed by finite substances, followed by modes. As we mentioned earlier, finite substances are bodies and minds, while modes are modifications of body and mind, like color, shape, size, imagination, idea, will, etc..."
Objective reality, pertaining only to representations (which have a low formal reality, being modes), refers to the formal reality of the object of the idea/representation if the idea existed. For instance, the idea of God has a low formal reality but a high objective reality.
Now, Descartes's argument relies on two notions, elucidated in the first page of Sinkler's paper in the Canadian Journal of Philosophy. First, the objective reality of an idea must originate from a cause with at least as much formal reality. The second, is that only a being possessing the qualities of God could produce the idea of God (this coming from the fact that the idea God has the highest level of objective reality, which can only correlate to a being with infinite formal reality, i.e. God). That the ultimate cause must be at least as "perfect" as its effects is another scholastic presupposition, as explained in the aforementioned commentary: "According to Descartes, something with a certain degree of objective reality must ultimately be caused by something with that degree of formal reality... If we trace the causal chain far enough back, we will find a cause with as much formal reality as the idea has objective reality. If the Meditator can locate an idea that has more objective reality than he has formal reality, he can conclude that there must exist something outside of himself which had to create the idea".
Descartes's argument is really a version of the "cosmological argument", as mentioned in the article from the philosophy Journal. He adopts ideas with scholastic origins which would have been understood at the time. To the logical flaws of the cosmological argument (which is now considered invalid). Descartes adds some problematic reasoning of his own, the so-called Cartesian Circle:"Descartes first argues from clearly and distinctly perceived premises to the conclusion that an all-perfect God exists; he then argues from the premise that an all-perfect God exists to the conclusion that whatever is clearly and distinctly perceived is true".