Electrodynamics plays a central role in physics undergraduate and graduate education for two reasons. One is practical, that modern society depends critically on electromagnetic devices of all kinds: for power generation and power distribution, for heating and lighting, for communication (radio, TV, Internet), for computation, for sensors, and for electronics that allow all kinds of devices to be controlled.
A second reason for the importance of electrodynamics is conceptual: electrodynamics provides an important example of the field concept, that there are spatially extended continuous fields that evolve on their own. The field concept helped to solve a problem that frustrated Isaac Newton and many other scientists around his time, which was how to explain "action at a distance", in which some object (say the Earth) affects some other object far away (say the Moon), even though the objects are not in direct contact with one another. The idea is that an object that has mass or an electrical charge generates a field that fills all the surrounding space, and remote objects then interact with this field in their vicinity. The field concept was especially central to Maxwell's great discovery that light was an electromagnetic phenomenon that involved the propagation of electrical and magnetic fields through a vacuum, in the absence of any charges or currents.
Physics 362 unifies, clarifies, and extends much of what you learned in an introductory physics course about electric fields, magnetic fields, the interactions of charged particles with E and B fields, and light. In your introductory physics course, you learned many different formulas that covered many different examples of electric fields, magnetic fields, and light. 362 shows that these many formulas can be derived from a single concise set of equations called the Maxwell equations, that summarizes all classical (pre-quantum) knowledge of electricity and magnetism. The course also spends a fair amount of time teaching new mathematical methods that can be used to find solutions of the Maxwell equations in a variety of experimental and engineering contexts. These mathematical methods turn out to be broadly useful in many other scientific and engineering contexts.
A beautiful insight that 362 discusses is that the Maxwell equations and Einstein's theory of special relativity are closely related. Until Einstein came along, electric and magnetic fields were treated as different physical objects. But the theory of relativity shows that electric and magnetic fields are really a single object, and whether one observes a magnetic field or an electric field or some combination depends purely on the frame of reference of the observer. This connection between relativity and electrodynamics played an important role later on when physicists succeeded in developing a quantum theory of electromagnetic fields called quantum electrodynamics, which is one of the most successful and accurate theories yet developed.