Most, but not all, components monitored by an OBD II electronic control module (ECM) have a 2-trip detection logic, where the ECM has to see the problem on 2 consecutive trips before it illuminates the malfunction indicator light (MIL). An example of a component that does not have 2 trip detection logic would be a knock sensor. If the ECM does not see a signal from the knock sensor, it will retard the timing the maximum amount because constant knocking can damage the engine.
For components with 2 trip detection logic, the ECM records either a good or bad signal for 2 trips. If the memory is cleared, the memory locations for the component are empty and are neither good or bad and so the ECM indicates that it is not ready yet because it has not gone through the 2 trips necessary to fill the memory locations. There is no additional "history" beyond the last 2 trips, which is why you get the "not ready" status until the 2 trips have occurred.
There are specific parameters for the ECM to count a driving session as a "trip." Basically, the engine, coolant, O2 sensors, and catalytic converter have to reach operating temperature and all of the sensors have to have a chance to sense whatever it is that they are supposed to be sensing. For example, just starting the car and letting it warm up won't let the vehicle speed sensor sense how fast the vehicle is moving. The factory repair manual has a list of conditions that have to occur before a driving session qualifies as a trip.