Real time means that responses occur in time, or on time. With non-real-time systems, you do not have any way to ensure that your response occurs within any time period, and operations may finish much later or earlier than you expect them to. In other words, real-time systems are highly deterministic, which guarantees that your operations occur within a given time. Real-time systems are predictable.
For a system to be a real-time system, all parts of it need to be real time. For instance, even though a program runs in a real-time operating system, it does not mean that the program behaves with real-time characteristics. The program may rely on something that does not behave in real-time such as file I/O, which then causes the program to not behave in real-time.