The way the petcock works is considered a "safety" feature. Old style bikes with on-off petcocks, are easy to oops and forget to switch it off. Which, due to the imperfect real world, can lead to the carb overflowing. The vacuum triggered action of our petcock is suppose to stop that forgetfulness.
But........ if the bike sits long enough the gas can evaporate out of the carb. When starting in this condition, the vacuum switch doesn't stay open long enough to get gas in the carb fuel bowl. Thus, there is the PRI or 'prime' postion to flow fuel into the carb before starting. Flow it for a little then switch to on.
In the ON position, there is a small tube that raises the inlet up a bit so that when riding and you get to that level and "run out" of fuel, you can switch to RES (reserve) and have 0.6 gallons to get to a gas station.
The "run out" of fuel manifests itself two ways. In "city" stop & go driving, you will notice the idle RPM's dropping, then just a couple of minutes later you will start to have the "blah" no power when hitting the throttle, and/or a bucking or mis-fire condition. On highway cruising, you go right to the Blah/bucking/ mis-fire.