The term real time can be a little misleading because it implies something that happens in a very narrow window of opportunity. What this term really means is that the appropriate users are notified of relevant events in a timely manner. Compare this to the common way that users normally make decisions, which is running reports based on data that's likely too old. For this reason, real-time enterprise is often referred to as event-driven enterprise.
A related capability is alerting users if a defined threshold is exceeded. For example, if the inventory falls below an acceptable boundary, the user should be notified, commonly via email. Note that the inventory threshold is often the result or consequence of one or more business processes. Thus, these alerts are not defined in isolation but instead are tied to one or more business processes.
Unfortunately, early attempts at building event-driven enterprise systems resulted in too many system-level events being forwarded to users, creating data overload for those users. Many systems lacked the capability to correlate the individual events at the system level to produce an event at the business level. For example, when a server goes down, the user may need to know whether that server is simply providing hosting for internal demo sites or running a mission-critical procurement application, whose performance is enforced by a service-level agreement with major customers. Obviously, the latter would be a higher priority and would need to be addressed immediately.