Why does iron float in mercury?

The only reason for this is density.
All objects have volume, meaning the object occupies some space. When an object is dropped in a liquid, the object displaces an amount of liquid equal to its volume, if the mass of the displaced liquid is greater than the mass of the object, then the object will float on the liquid, but if the mass of the object is greater than the mass of the displaced liquid, then the object will sink in the liquid.
Now density of iron is 7900 kg per cubic meter and density of mercury is 13600 kg per cubic meter. If the iron is placed on liquid mercury, the iron will displace its volume of mercury which has a greater mass than the iron, as a result of which the iron will float on the mercury.
Similarly iron sinks in water as water is less dense than iron.
Density of water: 1000 kg/m^-3
Density of iron : 7900 kg/m^-3
Density of mercury : 13600 kg/m^-3
Density of Glycerin : 1260 kg/m^-3
Density of Glycerin : 1260 kg/m^-3
Density of soybean oil: 927 kg/m^-3
Density of diesel : 800 kg/m^-3
Density of gold : 19300 kg/m^-3
Density of silver: 10500 kg/m^-3