The (problem/application) domain models a part of the real world having similar needs and terminology, and where a system instance may be a (partial) solution to some need (the problem). It is not specific to a particular system or system family, but rather to a market segment. It covers common phenomena, concepts and processes that need to be supported to solve the problem, irrespective of particular system solutions.
Note that the domain is like a type; it is a generalised concept covering the common features of many domain instances. Hence the Domain is not a set of occurrences, but a general pattern for one occurrence.