Vitrification is a technology that is used in the embryo and egg freezing process so that they can be stored for later use. It is a technology that has many uses outside of fertility care with egg and embryo freezing, as it allows something with a crystalline structure to be converted into something very smooth. The classic example is the creation of glass using sand (which is crystalline) as the main ingredient. Other examples include the manufacture of china plates and cups (also using sand), cotton candy from sugar (also crystalline) or ice cream which is smooth to the taste and contains no ice crystals despite its frozen state.
When we freeze cells in a lab, the main focus of the process is avoiding ice crystal formation as the fluid in the cell cools to subzero temperatures. Ice crystals pose 2 significant and deadly problems for cells. First, despite its beauty, an ice crystal is razor sharp and will readily shred any cell membrane, killing the cell. Second, as water in the cell turns to ice, it expands in volume, rupturing (killing) the cell. As a result, processes must be developed that allow cells to be frozen while avoiding the formation of ice. This science, called cryobiology, has come up with 2 methods that work well with human embryos, slow freezing and vitrification.