The egg and sperm meet in the outer third of the Fallopian Tube. Once they join the two cells begin to rapidly multiply. This stage of gestation is known as the zygotic stage and your baby is known as a zygote. From here the baby will become a blastocyst and implant in the uterine lining. The inner cells develop into the embryo while the outer cells will nourish your baby and become the amniotic sac and the placenta.
Photo © A.D.A.M. in Fetal Development