Kripke is concerned to keep a clear distinction between epistemological and metaphysical/logical categories. For Kripke, a priori and a posteriori belong to the former, necessary and contingent to the latter. These distinctions are important for him because they allow him to do a number of things: (a) address Frege's puzzle with a Millian, Direct Reference account of names, (b) offer a defense of strong or de re essentialism, which is crucial for the theory of names he defends, and (c) assist him maintain his version of Referential Realism.
IN a nutshell, he solves Frege's puzzle by arguing that while certain claims about meaning are known a priori it doesn't follow that they are necessary; if necessity is the mother of triviality, it is possible for something to be known a priori, but still be informative--in short, a priori contingent. Likewise, something may be necessary but known only a posteriori. Essentialism is both supported by and adds support to Kripke's theory of names and his Referential Realism by allowing us to have a non-language specific mechanism for connecting language to the world; it provides a means for us to connect language to the world without the heroics of Locke's Causal Representative Theory of Perception which accounts for language's power to represent the world by connecting language to our ideas which, in turn, are caused in us by the world itself. Let's look at the distinctions and some of their implications and difficulties.