Administrative Law has existed as an upper-level course in law school for decades. Curiously, it is not a class which necessarily follows from the U.S. Constitution, nor is it one with which many law students are familiar before law school (unlike, for example, Criminal Law). And yes it is a course important to the legal careers of almost all practicing lawyers. Why?
The concept of Administrative Law emerged in the United States, at least in part, as a response to the exponential growth in social, economic, and technological complexity since the drafting of the U.S. Constitution. This increased societal complexity makes it quite literally an impossible task for legislatures to draft every rule, and for a single executive (the President-as-one-person) to oversee the execution and enforcement of every law. This creates a challenging legal question -- what, then, do we do as a society? Do we leave certain social problems unaddressed until the Constitution is amended, or do we create institutions capable of managing that complexity through some other mechanism?
The practical answer to this, with which almost every citizen is now familiar, is the creation of "agencies." (Hint: if you have a Driver's License, have attended any public institution of higher education, received any type of government benefit, served in the armed forces, or voted, you've experienced and interacted with an "agency.") Most of these are created by statue, although some are created by Executive Order. In either case, however, many important questions exist regarding the extent to which Congress can "delegate" power to "agencies," the rules surrounding agency procedure, and what constraints must be placed on agencies to ensure that Constitutional guarantees are upheld. These are not hypothetical questions -- indeed, they have become the topic of political debates in almost all Presidential elections in recent memory.
The Administrative Law course tackles these questions both from a theoretical perspective and from a practical one. The theoretical perspective helps students understand why these Constitutional issues matter, and how to identify and answer what types of new questions will emerge. The practical perspective teaches students what are the current rules and doctrine in force "on the ground" today and the history of how these limitations developed. Together these two perspectives prepare students not just for the next five years of their career, but for the next 50.
An example syllabus is available here.