Time of a bit of a long-winded explanation...
Often in flash photography, we overpower the existing light so that all of our illumination comes from the flash. There are certain times that we try for a combination of ambient light and fill light; and use of fill-flash, is one fairly basic example of where we use a combination of ambient and flash. Fill flash does not necessarily mean we are "dragging the shutter". Dragging the shutter is essentially having a shutter speed that is slower than the synch speed of the camera, which allows more ambient light to affect the image. Let me show you a couple of examples of this:
1. Often when we do a flash shot of the interior of a building, the ambient light outside is so bright that light coming in through the windows results in overexposure. If we set our camera speed so that the light outside is properly exposed and then use a flash inside (I do this in manual mode) to light the inside of the room, we get a shot that is correctly lit for both light sources:
The interior was lit by two Speedlights; you can see some of the glare in the window' that comes from my main Speedlight. This shot was take at 1/25 at f/5.6 at ISO 200. The camera flash sych speed is 1/200 sec, so by shooting at 1/25; this is "dragging the shutter". I used a shoot through flash as my main light and stand-alone flash to light up the back hall.
The second example was shot in a way to light my subject for proper exposure, but selected a shutter speed and aperture that underexposed the background so that the wall of the hut appeard to be fairly dark. This shot is at 100 ISO at 1/125 at f/2.8. The flash synch speed on the camera is 1/250 sec.
So by shooting at 1/125, I was "dragging the shutter". I used a Rogue Flashbender as a light modifier in this image.