What is Administrative Law?

Legal Definition
Administrative law is the body of law that governs the activities of administrative agencies of government. Government agency action can include rulemaking, adjudication, or the enforcement of a specific regulatory agenda. Administrative law is considered a branch of public law. As a body of law, administrative law deals with the decision-making of administrative units of government (for example, tribunals, boards or commissions) that are part of a national regulatory scheme in such areas as police law, international trade, manufacturing, the environment, taxation, broadcasting, immigration and transport. Administrative law expanded greatly during the twentieth century, as legislative bodies worldwide created more government agencies to regulate the social, economic and political spheres of human interaction.

Civil law countries often have specialized courts, administrative courts, that review these decisions.
-- Wikipedia
Legal Definition
Branch of law governing the creation and operation of administrative agencies. Of special importance are the powers granted to administrative agencies, the substantive rules that such agencies make, and the legal relationships between such agencies, other government bodies, and the public at large.
Overview
Administrative law encompasses laws and legal principles governing the administration and regulation of government agencies (both Federal and state). Such agencies are delegated power by Congress (or in the case of a state agency, the state legislature) to act as agents for the executive. Generally, administrative agencies are created to protect a public interest rather than to vindicate private rights.

Governmental agencies must act within Constitutional parameters. These and other limits have been codified into statutes such as the Federal Administrative Procedure Act (FAPA) and state analogs.

The FAPA is a remedial statute designed to ensure uniformity and openness in the procedures used by federal agencies. The Act is comprised of a comprehensive regulatory scheme governing regulations, adjudications, and rule making in general terms. The FAPA is the major source for federal administrative agency law, while state agencies' administration and regulation are governed by comparable state acts.
Legal Definition
That branch of public law which deals with the various organs of the sovereign power considered as in motion, and prescribes in detail the manner of their activity, being concerned with such topics as the collection of the revenue, the regulation of the military and navni forces, citizenship and naturalization, sanitary measures, poor laws, coinage, police, the public safety and morals, etc. See Holl. Jur. 305-307.
-- Black's Law Dictionary