The key terms, "analytic," "synthetic," "a priori," and "a posteriori,"
are given-the most cursory definition. Kant merely states, with
no real demonstration, that there are synthetic judgments a priori;
to the uninitiated reader it is exceedingly unclear why so long and
difficult a book should have been devoted to the answering of so
dubious a question. Indeed, it soon becomes clear that the question
is a very inadequate representation of the subject of the Critique,
for one of Kant's principal aims is to prove that all judgments,
a posteriori as well as a priori, are in need of explanation and
That's why Kant wrote the Prolegomena to any Future Metaphysics in 1783, to provide definitions for such obscure terms. I did not read that work until much later, so I had to make due with skipping back and forth between Kant's Introductions to the Critique of Pure Reason and the main text of the book. This method wasn't entirely successful, however. But I did learn that Kant's goals were not as many so-called philosophers claimed them to be.
"Analytic" simply means it was taken apart. "Synthetic" simply means it was put together. "A priori" means before the fact. "A posteriori" means after the fact.
It gets confusing when Kant states that there are synthetic judgments a priori. And then this is further confused when he explains that "a priori" does not indicate before any particular fact, but before any and all facts. This terminology indicates to some less-than-worthy philosophers that Kant believed that some knowledge is innate, i.e., "before any and all facts" and thus makes our knowledge of these facts possible. This interpretation however ignores Kant's transcendental distinction which was made in the Transcendental Aesthetic: the distinction between appearances and things-in-themselves.