This is the flow generated during the inspiratory phase. Much of the time it is irrelevant from the diagnostic point of view, as it is something wholly machine-related. The ventilator generates this flow.
In a volume-controlled mode of ventilation, the inspiratory flow waveform is rectangular (as the machine delivers a steady flow of gas, waiting for the target volume to be achieved).
In a pressure controlled mode, the inspiratory flow waveform is decelerating, as the machine delivers just enough flow to produce the desired pressure.
Peak expiratory flow
The rate of expiratory flow is determined by the resistance of the airways and the elastic recoil of the lungs and chest wall.
The height of this waveform reflects these features; a low expiratory peak flow suggests there may be some bronchospasm.
In the same way as peak flow measurements can be used to assess an asthmatic, so can the expiratory peak flow of a ventilated patient inform you about the airway resistance.
A low expiratory flow obviously suggests you have an airway obstruction (or, more freakishly, an abnormally over-compliant chest wall)
Similarly, if your expiratory flow is prolonged, your airway resistance must be increased.
Furthermore, if the flow does not reach zero by the beginning of the next breath, there must be gas trapping (i.e. the patient has not finished exhaling fully before they are forced to take another breath).
In pressure-controlled ventilation which is time cycled, one can see the flow curve return to zero during inspiration.
This means that the target pressure has been achieved and that there is no flow (a tidal volume is breath-held) for some period of time.
If the flow curve does not return to zero before expiration, there is still some room to go with the pressure; a larger tidal volume can still be achieved.