What property is used to separate gold from sand when they swirled in a pan filled with water?

Density.

Gold has an extremely high density relative to the rest of the sand in the pan and will therefore fall to the bottom as one swirls the pan around. The water is there to provide a means by which to circulate the dirt mixture and eliminate the "sand" (the sand gets suspended in the water and spills over the sides of the pan as it is swirled).

And that's pretty much panning for gold.