A 'domain', in Artificial Intelligence or machine learning, is a problem class on which an AI program can be targeted. Face recognition is a 'domain', as is playing chess, or driving a car. Each of these domains presents characteristic options and modes of action for accomplishing the task: a Go game can be won by outputting good Go moves, a car can be moved safely to its definition by turning, accelerating, and braking. The real-world domain is the superdomain that contains all of reality. In reality, you could try to win a chess game by making funny faces to distract the opponent, and a driving problem has solutions like 'work for a salary and use the money to pay for an Uber'. If you can reason like this then you are acting in the 'real-world domain'.
Being able to act in the real-world domain is distinct from realistic domains. Driving a robotic car is a realistic domain: solutions must be computed in real-time, everything is continuous rather than turn-based, a deer could wander across the road at any time, sensors and knowledge are imperfect, and sometimes a tire blows out. Even so, a standard robotic driver that faces this class of events will act through the medium of steering and acceleration. If instead the robotic driver switched to running a hedge fund and hired a human to drive the car using the money it earned, it would have taken advantage of such a breadth of options that the only domain wide enough to contain those options is 'the real world', reality itself where anything goes so long as it works.
Acting in the real world is an advanced agent property and would likely follow from the advanced agent property of Artificial General Intelligence: the ability to learn new domains would lead to the ability to act through modalities covering many different kinds of real-world options.