In some cases storing of sperm or embryos is needed. For sperm it happens when the male will not be available a time of IVF/ICSI operation or the male has undergone a testicular biopsy and the sperms found will be stored for future use in IVF/ICSI or the male is going for cancer treatment which might destroy testicular tissue.
For embryos sometimes there are situation when there many embryos produced and after replacing some of them in a cycle the ones left are stored for another cycle. Cryopreservation is also useful if anything cancels the embryo transfer part like inability to arrive at time on embryo transfer day or the woman has a weak endometrium or has hyper stimulation.
The embryos are mixed with a cryopreservent that protects the embryo and then the embryo is vitrified i.e. frozen to a degree lower than 15 thousand under zero in few seconds (on the contrary to the conventional cryopreservation where it took longer time for embryos to freeze allowing ice crystals to form inside them which destroys them ). Thawing and replacing the embryos involves defrosting the embryos and removing the cryopreservent material then replacing the embryos inside the uterus.