Kant's famous distinction between analytic and synthetic judgments seems to have left much of the tradition after him wondering about its value, and so, its meaning. It seems obvious that concepts contain whatever they do (analytic), and when we learn something new we expand our concepts (synthetic), but how is this important?
The distinction between analytic and synthetic seems to have been abused after Kant, and began to suggest that propositions themselves were either analytic or synthetic when really Kant insists that what is important in any particular case is what we actually thought in these judgments. (This being said, it was of no use to attempt to clarify language through this distinction.)
It seems to make sense to consider the value of the distinction between synthetic and analytic to reside in the context that was so crucial for them: critique of pure reason (the special science). What was important to Kant about the distinction between analytic and synthetic was how it provided clearer access to the problem of synthetic a priori judgments. It will help to consider other disciplines where the distinction is applicable, but not necessary for any work.
Mathematics and physics entirely consist of knowledge from synthetic judgments, but this does not mean they should concern themselves with the distinction between analytic and synthetic: mathematics uses pure intuition to guide itself, while physics uses experience (and mathematics). These sciences have material to guide them that clearly shows the ground for their synthetic judgments, but also makes it unhelpful to know when these synthetic judgments are in effect: they always are.
On the other hand, metaphysics has no material to guide it in its use of pure concepts, and generates pure concepts, and so if we concern ourselves with the possibility of metaphysics it is necessary to test to see if pure concepts can be employed in the extension of knowledge. Then, it will be necessary to discover what the pure concepts are, and for this the distinction between analytic and synthetic is crucial.