The fusion of the sperm with the egg results in the formation of a zygote that develops into a new offspring. Twins refers to the two offspring which are a result of the same pregnancy. They are of two types. Monozygotic twins are a result of the single zygote (formed by the fusion of one egg with a single sperm) spiltting into two embryos forming the identical twins. Dizygotic twins are a result of two eggs fertilized with two different sperms forming the fraternal twins.
Identical twins are genetically simliar. The genetic material is derived from the same embryo and thus, the DNA of the identical twins are nearly identical. The spilitting of the embryo formed results in the separation of the same genetic material or identical DNA getting incorporated into the twins making them look alike in majority of the cases.