Operations research (OR) uses mathematical tools to solve problems of industry and government. The mathematical techniques used fall into the general headings of Optimization and Probabilistic Analysis. Optimization includes such topics as discrete optimization and graph theory, linear programming and constrained nonlinear optimization. Probabilistic analysis includes the analysis of queues, simulation, and statistics. Operations researcher range from the very applied to the very theoretical. The applied OR's generally take real world problems (see below), model them as mathematics, and use mathematical tools to solve them. Theoretical OR's will for the most part ignore the real world and spend their time learning more about the mathematics that underlies the techniques used by the applied practitioners. Theoretical OR's can be indistinguishable from other theoretical mathematicians. There are, of course, many people between these two extremes who work both with theory and applications.
It is not necessary to be interested in all areas of operations research to become an operations researcher. People often go into OR with a specific area in mind, and learn something about the others on the way. On the other hand, many people go into OR because they are interested in applying mathematical ideas to business and industry and don't know exactly which aspects interest them most.
Some applications of operations research: bus scheduling, garbage truck collection routes, optimizing the product mix for a company, analyzing lines at a bank, scheduling the portions of a big project, inventory theory, plotting political campaign strategies, constructing warfare models.
Warning: If you ask three different OR people what OR is, you will most likely get three different answers. Also, if you know what you would like to do and you think it is OR, it may well go under another heading at a different university. Programs that are similar to ``operations research'' have names like Industrial Engineering, Management Science, Modern Applied Mathematics, Systems Science, and Systems Engineering. You must look closely at each individual program in order to decide if it includes the areas you are interested in.