All these settings are found along the top of the screen here, when in brush mode:
Note that opacity and flow settings made in the brush pallet will override these settings:
All three settings, opacity, flow and airbrush, are effects controlled by your pen having continuous contact with the tablet surface.
So with opacity at 50%, no matter how many times you go over the same area, as long as your pen does not leave the tablet surface the opacity of the stroke will remain at 50%. However, as soon as you take the pen off and reapply, the stroke opacity will have a cumulative effect:
Flow recognizes how many times you go over the same area even if the pen remains in constant contact with the tablet surface, and will make the stroke darker and darker. Just like going back over the same area of paper with a pencil. As this is close to how real media work, I find it a very useful effect as it feels and looks more natural (flow set at 1%):
Where the flow option works on movement, airbrush works on time. Just push your pen onto one spot on the tablet and hold it there. The longer you keep it touching one area, the darker the brush stroke will become (note flow still at 1%):