The embryo sinks down and reaches into soft and thick lining of the uterus. The embedding of the embryo in the thick lining of uterus is called implantation.
The implantation occurs in the uterus.
The placenta is a grows into a disc like structure between uterine wall and the embryo. Placenta forms finger like projection called villi towards embryo. This creates large surface area for the exchange of glucose and gasses between mother and embryo.