The density of a liquid is the mass of a unit volume of the liquid. In terms of SI units density is expressed as kg/m^3, though it is commonly expressed in terms of g/mL.
If the density of an unknown liquid is known to be 1 g/mL, it is not possible to reach at any conclusion about what the unknown liquid is. Water is one of the liquids that at a particular temperature has a density of 1 g/mL. But this cannot be used as a method to identify any given liquid as water; if there are a limited number of choices and there is a large difference in each of their density it may be possible to identify water from the group of liquids by measuring their density.