I'm not sure...that sounds like something specific to Nikon or that camera.
I think the sync speed you are seeing in the camera's menu is the 'default' that you can set it to. If I'm correct, this would make the camera use a shutter speed of 1/60 (or whatever) when you have the flash on and it's in an auto mode.
The max sync speed is determined by the design of the camera (should be easy enough to find out). So all you really have to know, is that when using flash, you need to keep the shutter speed under that speed. Some cameras will prevent you from setting a faster speed, while the flash is attached and turned on.
Now, it should be noted that shutter speed has no affect on the exposure from the flash. In a completely dark situation, you would get the same flash exposure at 1/15, as you would at 1/250. The flash fires much faster than that so the shutter speed isn't important. The aperture and the power of the flash, are the two things that will control the exposure from the flash.
However, we aren't always in completely dark situations. There is often some sort of ambient light. The exposure from the ambient light will be affected by the shutter speed (and the aperture) just like on any shot without flash. So basically, every flash shot is really a double exposure...one flash exposure and one ambient exposure.
Now because the shutter speed doesn't effect the flash exposure, you can use the shutter speed to independently control the ambient exposure when using flash. The longer the shutter speed, the more ambient exposure you get. Using a longer shutter speed with flash, is often called 'dragging the shutter'. This is handy when your subject is fairly close to you but the background is not. A dark wedding reception hall, for example. The flash will light up the people in front of you just fine...but the flash can't light up the background as well. If you use a fast shutter speed, they will look like they are in a cave because the background will be very dark. If, however, you use a slower shutter speed (and there is some ambient light) then the background will get more exposure and they won't look like they are in a cave. The flash exposure will not have changed because the aperture and flash power are still the same.
The way I do this is to shoot in manual mode when in this situation. You set the aperture based on the DOF that you want, the flash (if it's a dedicated TTL flash) will adjust it's power to suit the aperture. Then you can set the shutter speed to get the amount of ambient exposure you want.
It should be noted that if you use a long shutter speed and there is ample ambient light...you will still get motion blur like you would without flash. Sometimes this looks good in combination with the flash exposure...but sometimes not. You need to compromise between how much ambient exposure you want the shutter speed you can get away with.
One more variable....ISO. The higher you set the ISO, the more ambient exposure you can get for a given shutter speed & aperture. It also lets the flash use less power, so you get faster recycle times and longer lasting batteries. For this reason, I will usually use ISO 400 or even 800 when using flash.