How does metering/exposure work when using a flash?

[TMR Design]

I am doing some experimentation with shooting indoors and using a flash. Normally, even on a bright sunny day I don't get enough light in most of my apartment to take pictures with good exposures.

After trying many different things I found that with ISO 400, 1/160 shutter speed, f/4.1, flash on but flash output dropped 2 stops? (not sure what the units are representing) and set on 2nd curtain I get well lit, good indoor shots that don't appear washed out or too bright or reflective from the flash. Obviously if I leave all the settings the same and turn the flash off the LCD appears very dark and would be completely underexposed, and in Tv mode the camera still keeps the f/4.1 setting when the flash is on or not.

So my question in all of this is: How is the camera metering and setting exposure when the flash is on? On the A620 there is a flash output control but no other controls or indicators giving info about the flash setting.
I am trying to get a handle on what technically is happening in the camera and flash to bring it all together.

[dhbailey]

I wish I could give you a technical explanation, but the best I can do is to offer a layman's explanation, which if it's wrong I'm sure someone will jump in with the correct explanation:

The camera knows how bright the flash will be, and it assumes that you're smart enough to be shooting a subject within the stated range of the flash, so it can automatically set the exposure correctly based on your shutter speed, or set the shutter speed based on your manually set aperture, if you're in Av mode.

But since the camera can't know exactly what you're shooting, the camera could be overexposing or underexposing the scene, which is why we can adjust the Flash Exposure up or down so the camera captures either more or less light as we choose.

Good thing this is all instantaneous and doesn't cost us anything, huh? I remember many a film shot wasted because of improper exposure, even with a flash.