It's really difficult to succinctly explain, partly because making sense of the criticism in full requires understanding Kant's epistemological and metaphysical assumptions lurking in the background. I'm not an expert on Kant by any means, but I'll do my best.
Perhaps the easiest starting point is to see that Kant accepts Hume's arguments that the causal principle cannot be justified by conceptual analysis or experience. Regarding the former, there's no strict contradiction in supposing some event is uncaused. With the latter, Kant agrees with Hume that experience cannot establish the necessity or universality of the causal principle (every event must have a cause).
So if the causal principle is knowable, it must be synthetic yet a priori. Many philosophers have found the very notion of synthetic a priori knowledge mysterious if not totally incoherent; after all, how could pure reason establish substantive truths about mind-independent reality without the aid of experience?
Kant attempts to provide an answer in arguing that synthetic a priori truths express conditions of the possibility of experience. In Kant scholarship, as far as I can tell, there's no consensus as to what exactly Kant means by this, but one traditional answer is something like the following: our faculties structure experience such that certain synthetic principles are necessarily true (in brief, objects of possible experience are causally interacting spatiotemporal substances).
If Kant's arguments work, they establish the relevant synthetic a priori principles hold for appearances (roughly, things considered in relation to subjects with our cognitive faculties), yet for the same reasons cannot be applied to things in themselves (roughly, things considered independently of those relations). If that is correct, then clearly the causal principle cannot be applied beyond the existence of the spatiotemporal world to establish the existence of God, so the cosmological argument fails.
Hopefully that gives you a general idea, but keep in mind this is extremely oversimplified. To get a a complete picture, you really just need to read the CPR along with a good companion book.
Sebastian Gardner's Philosophy Guidebook is really clear and thorough. I've used it many times.
This book by Sebastian Gardner is helpful for first-time readers.
Although Deleuze is a rather controversial figure in philosophy, I think his book on Kant's critical philosophy is also quite good and easy to digest.
I would suggest beginning with these two.
Check this out. It's much clearer and shorter.
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