This is not all the same exact shot, but it was the same location all at the same time and it'll give you a good general idea. This is all around 6PM with strong direct sun coming in the WEST facing of our house which is wide open to get the harsh afternoon sunlight.
First a shot with no flash at all. Obviously you're completely hosed here with a total blowout.
Next is 1/125s with flash, and you're still hosed with a total blowout.
I did 1/500s with flash next and was going to go back and do 1/250s but unfortunately the sun dipped behind a cloud and it wouldn't have been consistent. Obviously this is much better and you're able to completely neutralize the harsh light and get a balanced exposure on the face.
Here's 1/250s with flash from a slightly different orientation with the sun coming directly in the window from the deck. This is "adequate" for harsh light and you can get the light you need on the face with a reasonably balanced expsoure, but the deck is still completely blown out.
And then here's
1/500s with flash two shots later. I actually don't like the shot (bad expression, lol) but it's as close to the same exact shot I had as the baseline at 1/250s. You can see now that the deck is actually balanced out in the exposure thanks to the 1/500s sync. You can't really see it in this one, but there's actually detail on the top of her head now whereas it was sorta washed out in the previous.
And then here's two more at 1/500s sync.
At least for fill flash, you only really need 1/500s in truly HARSH lighting conditions. In our house especially with the direct WEST facing where we get really harsh light in the evenings, the 1/500s flash sync on my D40 is invaluable. If you're trying to freeze action and 1/200 or 1/250s won't cut it, 1/500s is invaluable too. My daughter on a swing is quick enough to really push the limits of 1/250s, and if you combine that with some really harsh light, 1/250s becomes useless. I had to toss a whole session of swing photos from my D80 once because it only does 1/200s flash sync and it just would not balance out the harsh light like my D40 will. The faster sync will also let you shoot at a larger aperture for less depth of field which is useful for portrait photos, although you can just use a neutral density filter for that as somebody already pointed out.
Daylight 1/500s flash sync photos can start to look "too" flashy if you don't truly have really harsh light, so you'd either want to back the shutter speed off a bit by a stop to 1/250s such that you're proportionally capturing a stop more of the natural light and a stop less of the flash's light if that's still fast enough to freeze whatever action you're capturing, or just stick it at 1/500s but use some negative flash exposure compensation so that it backs off the flash power a bit and then either shoot at a larger aperture or a higher ISO to again proportionally capture more of the natural light and less of the flash's light.
I'm still learning flash technique so if I'm off on any of this, someone please feel free to correct me.