So far, the explanations presented are pretty accurate. However, as a biochemist, I have a good background surrounding the science around stem cell research, and I will try to answer questions asked thus far and expand on certain things.
1) Stems cells are unspecialized cells, meaning they do not have a cell function, but they are capable of giving rise to specialized cells in a process called differentiation. The most obvious example of this is the embryo shortly after conception. At this point, one cells divides many times, forming a ball of cloned cells. Later after conception, the divided cells begin to clump together to form a specialized cell, like heart, muscle, and lung cells.
2) The reason scientists in the U.S. have been fighting to gain more funding by the government for embryonic stem cell research is because of its unique properties, which are similar but different from adult stem cells. Embryonic stem cells can become ALL cell types of the body, while adult stem's plasticity is limited. Furthermore, embryonic stem cells are more easily cultured in the laboratory because adult stem cells are rare in mature tissues.
3) Most embryonic stem cells that scientists used are made IN VITRO, meaning the egg is fertilized outside of the human body (i.e. a test tube baby). Thus, images popularized by conservatives of researchers killing babies to get stem cells is false.
4) This research are has HUGE implications for the medical fields. As many of you have already stated, stem cells can be used to grow specialized tissues, which can then be transplanted into human subjects. For example, people with Type I diabetes cannot produce insulin because their insulin-producing cells are destroyed. Theoretically, one can culture healthy insulin-producing cells and transplant them into the diabetic liver.
The gains that can come out of stem cell research is practically endless.