A salt mine is a mine where salt is taken from the earth. Very often, this is done in the mountains. It is different from a salt evaporation pond, where salt is taken from salt water. Getting salt from different layers of rock in a mountain used to be a very dangerous job. The Romans used to sentence prisoners to this kind of labour.
Empty salt mines are used very often as a storage area, for example, for unused radioactive elements (from nuclear power plants). Salt mines are empty if there is no salt left to take, or if taking the salt that is left would be too expensive.