Metal density is higher than water density for two reasons: first, the atomic mass of most conventional metals is higher than the molecular mass of water. Second, metal atoms are held more closely together by metallic bonds than water, which is held together by hydrogen and covalent bonds.
To calculate density, the total mass of matter is divided by its total volume. For a constant volume, the higher the mass is, the denser the matter becomes. A cubic inch of steel and a cubic inch of water both occupy the same volume, but because the atoms in the cubic inch of steel are heavier than the atoms in the cubic inch of water, the density of the steel is higher than that of the water. Similarly, the smaller the volume occupied by a certain mass of material, the higher its density. A pound of wool and a pound of steel both have the same mass, but the wool occupies a much larger volume.
However, there are exceptions. Lithium, sodium, and potassium are metals that have specific densities that are lower than water, enabling them to float. This floatation is assisted by the hydrogen bubbles that form when these metals react with water.