Thanks for the bullet-speed replies!
But then what is the relation between the meter measurements
and my camera settings?
I feel like I've living in darkness all this time
In flash lighting, as mentioned, the flash output is a tiny fraction of the time your shutter is open. With flash, the flash output brightness (and/or location, as they're obviously related), and the f-stop you're shooting at, are the exposure variables of importance (ignoring the issue of using fill flash with ambient lighting).
So, if you want a particular f-stop (for DOF purposes or whatever), you have to change your flash output intensity instead of your shutter speed. If you have a set flash output for whatever reason, then you change your f-stop to get the right exposure (stop down if your flash is too bright, etc).
Shutter speed has no impact, because the flash virtually instantaneously "pops" and puts out all its light in a fraction of the time your shutter is open. Doesn't matter if you're at 1/60th or 1/200th - your film or sensor will catch the same amount of light from that instantaneous flash pop.