Egg, Sperm or Embryo freezing is a process called Cryopreservation or Cryoconservation.
What happens is that eggs, sperm or embryos are cooled down to very low temperatures, somewhere between minus 80°and minus196°C, and afterwards stored in so-called sperm banks, egg banks or embryo banks.
At the aforementioned low temperatures all biological activities in the cells are stopped. The idea is to be able to use those eggs, sperm or embryos at a later moment.
Use may be by the donors themselves, by others who get eggs, sperm or embryos donated, or by gestational carriers (surrogate mothers).