I´m going to start by guessing that by neuron cells you mean nerve cells, which are also called neurons. If that is not the case, then this is not the right answer. But if it is the case then please keep reading.

The cells of the nervous system, called nerve cells or neurons, are specialized to carry "messages" through an electrochemical process. The human brain has approximately 100 billion neurons! Neurons come in many different shapes and sizes. Some of the smallest neurons have cell bodies that are only 4 microns wide. Some of the biggest neurons have cell bodies that are 100 microns wide. (Remember that 1 micron is equal to one thousandth of a millimeter!).

So, where do these neurons comes from and how do they manage to make their billions of connections correctly in the human brain? It all starts with stem cells. First, in a process called cell proliferation, the number of stem cells begins to increase. Since the body needs to manufacture an absolutely huge number of neurons - 100 billion in the adult human brain - it has to start the manufacturing process early in an embryo´s development.

The next process involved in the origin of our nerve cells is called determination. During determination, the destiny of different types of cells is decided - and the destiny of some cells is to be a neuron. The final process in determining if a cell will become a neuron is called differentiation. During differentiation, a given population of neurons gives rise to subpopulations that are specific to the various parts of the nervous system. During this stage, the neurons continue to proliferate and migrate to their final locations, where they will make specific connections with other neurons.

Another cool thing about neurons is that they are the oldest and longest lived cells in the body! You have many of the same neurons for your whole life. Although other cells die and are replaced, many neurons are never replaced when they die. In fact, you have fewer neurons when you are old compared to when you are young. On the other hand, data published in November 1998 show that in one area of the brain (the hippocampus), new neurons CAN grow in adult humans.

Neuron cells are ectoderm, members of the outer layer of cells in animals (the middle layer, mesoderm, makes muscles, and the inner layer, entoderm, makes guts).

Neurons originally come from neural stem and progenitor cells before birth. These are "multipotent cells" in that they can differentiate/specialize into specific kinds of neuronal cells during the development of the embryo. Particularly, the cells of the nervous system are developed from the ectoderm (outermost layer) of the embryo. The particular pathway of development will depend on the kind of neural tissue that is being formed. For instance, the ectoderm eventually thickens and becomes the neural plate. The neural plate folds on itself and fuses to become the neural tube. The neural tube gives rise to different parts of the brain and the spinal cord. The neurons in different parts of the brain are actually different (specialized) according to what "jobs/tasks" that particular part of the brain has to do. As an example: cells in the cerebral cortex look different and different functions than those of the hypothalamus (this is just an example of two different structures in the brain).

In recent years, studies have also shown that neurogenesis (the production of new neurons) can also occur throughout adulthood -- but it appears this only occurs in special parts of the brain, such as the hippocampus and subventricular zone.