Embryonic development, or embryogenesis, is how the embryo forms and develops. This process starts after fertilization of the egg in the uterus. It occurs in the first 8 weeks of pregnancy during the first trimester. Of course, humans aren't the only ones who experience embryonic development, but the concept is the same. I will explain it to you in terms of the human embryo.

The newly fertilized egg is called a zygote. The cell keeps dividing by mitosis and becomes a solid balls of cells called a morula. The morula then becomes a blastula, which is a hollow ball of cells surrounding an inner fluid, called the blastucoel. The blastula then travels and embeds in the uterus (happens a couple days after the egg is fertilized). Formation of a gastrula follows blastulation, the formation of a blastula. The gastrula is a reorganized form of the blastula and includes three germ layers - the ectoderm, the mesoderm, and the endoderm - which surround the archenteron. These are "differentiated" cells for certain parts of the human body. The ectoderm becomes the neural system, the mesoderm is the basis for muscle tissue and cartilage, and the endoderm gives rise to the digestive and respiratory system. The archenteron isn't part of the three differentiated layers, but it forms the gut of the human (or animal). This whole process is almost the first trimester of pregnancy. After this, the differentiated parts develop and the heart beat forms and after 9 months you have a baby!

This seems like a lot of information but just remember:

fertilized egg (zygote) --> morula --> blastula --> embed in uterus --> gastrula --> differentiate into endoderm, mesoderm, ectoderm --> develop into baby!