(Comment: At this point, being a low tech household, I lack the ability to provide diagrams. But, I'll work on it...)
All God's creatures have stem cells. Birds do. Bees do. Even flowers and trees do. Mice do, and men do, and much of the research on stem cells has been done in mice, although, of course, it is also done now, and will be done much more frequently in the future, in men. So, we'll begin at the beginning. What is a stem cell?
A stem cell, according to the National Institutes of Health, is "a cell that has the ability to divide (self replicate) for indefinite periods - often throughout the life of the organism. Under the right conditions, or given the right signals, stem cells can give rise (differentiate) to the many cell types that make up the organism. That is, stem cells have the potential to develop into mature cells that have the characteristic shapes and specialized functions, such as heart cells, skin cells, and nerve cells."
What does all that mean? Fully mature tissues and organs are comprised of cells that are said to be fully differentiated. Every single cell within my body contains its own, complete copy of my genetic code, my genome. However, within each individual cell, only those specific parts of the code necessary for that cell to do its job are turned on. The rest of the genetic code is turned off. Thus, one of my liver cells looks like, and functions like, a liver cell because, within it, only those parts of my genetic code related to "liver cell-ness" are activated, while the rest of the genome is suppressed. My liver cell can only be a liver cell, and if it replicates itself, it can only make another liver cell. That's what is meant by differentiation. If I look at liver cells through the microscope, the morphology or microscopic appearance of the cells is that of liver cells, not, say, brain cells. This is true even though the two tissue samples may have come from the same individual and share the same genome. That is what is meant by "fully differentiated".
A stem cell is undifferentiated. Under the microscope, it doesn't look like any particular type of cell. It doesn't have the long axons of a neuron, or the striations of a muscle cell. It looks like the generic cell one finds illustrated in basic biology textbooks: a largish cell with a nucleus, where the DNA of the genome resides, and surrounding cytoplasm which house the little molecular machines which do the life work of the cell, all wrapped up in a cell membrane. But, this generic cell doesn't have any of the specialized molecular apparati or unique morphology of a fully differentiated cell. This lack of specialized form under the microscope reflects a lack of specialized function: the stem cell doesn't do anything special. It doesn't transmit nerve impulses or help you pick up the groceries. It just replicates, and makes more undifferentiated copies of its undifferentiated self. It does this self replication, under normal circumstances, within the organism. However, it can also be convinced to replicate itself in the petri dish. This property of self replication is not a property that fully differentiated cells, in general, possess. Mature neurons do not replicate under normal circumstances, nor do mature blood cells, mature muscle cells, nor many other differentiated cell types. This property, self replication, takes care of the first part of the NIH definition.
Concerning the second component of the definition, differentiation. We've seen that the stem cell is undifferentiated in its off-the-shelf form. What gives the cell importance is that it can develop and mature into any number of mature cell types. The most undifferentiated cell, for example, is the single cell zygote, the fertilized egg, the first step in the growth and development of a new creature. There is no qualitative difference between a human zygote, a mid term fetus, and a newborn. The difference is quantitative only. This fact regarding the nature of the human zygote is why the Church teaches it must be treated as a new human person, and must be kept in mind throughout the discussion on embryonic stem cells. The zygote is a totipotential stem cell, because it will go on to form every cell and tissue type within the body, as well as the placenta. Next on the list of stem cell types would be pluripotent stem cells. There are three germ cell layers in the early embryo: the endoderm (inner layer), from which parts of most internal organs develop; the mesoderm (middle layer), from which muscle, blood cells, and so forth develop, and the ectoderm (outer layer) from which skin, nerves, and the central nervous system develop. Pluripotent stem cells are stem cells which can give rise to differentiated cells from any of the three germ layers. Conversely, pluripotent stem cells don't give rise to placenta, umbilical cord, and placental membranes, like the totipotent zygote does. Embryonic stem cells, which will be the focus of next week's essay, fall into this pluripotent stem cell category. Finally, people speak of unipotent stem cells. These are stem cells which, under normal circumstances, give rise to mature cells of only one germ layer. In general, adult stem cells are unipotent. For example, a hematopoietic stem cell is a stem cell found in adults which can give rise to any of the red blood cells or white blood cells (mesodermal germ line origin) but not, under normal circumstances, an ectodermally derived skin cell.
So, some stem cells have greater flexibility and plasticity than others. Pluripotent stem cells can develop into a wide variety of mature cell types; unipotent stem cells have a more restricted menu. Can unipotent adult stem cells be convinced to be more flexible? Yes, but we get ahead of ourselves. The purpose of this week's little essay is to define stem cells in general. Next week, embryonic stem cells.
 "Stem Cells: Scientific Progress and Future Directions." Report prepared by the National Institutes of Health, June 2001. See Ch. 1, "The Stem Cell." available in downloadable format at http://stemcells.nih.gov/info/scireport/2001report