The meta-problem is a term to let us talk separately about "problems" to solve and a "problem" to figure something out. A meta-problem is the question of which problem we want to solve. The solution to a meta-problem will be a specific problem we have chosen to solve. The key features of a meta-problem are a clear statement of our goals and choices we have in pursuit of those goals. A meta-problem will define a set of "problems."

The idea of the "right" problem implies that other problems are "wrong." Usually, we only know a problem is "wrong" because there is some other problem we prefer to solve. Whether the alternatives are implied or explicit, it is by comparing one decision to another (or even the do-nothing option) that we can say a problem is the "right" one. The meta-problem approach is a framework for discussing those comparisons and the solution to the meta-problem is the selection of the right problem.

Describing a meta-problem starts with a list of goals. There are typically a lot of options to improve those goals, but in different ways or with different methods. You could think of each of those options as the answer to a specific problem, and the set of all of those options as a set of problems

You don't. Or at least, operations researchers work to develop mathematical models of decision making. People invariably have criteria they are unaware of until they try to ask a computer what to do. Even if you somehow did really know everything you care about, most of the time your choices will depend at least a little on some unknowns about the future.

Operations Research (OR) is a field that bridges engineering, mathematics, and business. One summary of the field is that it is focused on resource allocation problems. The tools we use to do so are math models of systems and decisions to help people understand how different choices we could make would impact outcomes we care about.