Stem cells are characterized by two unique abilities. For one they have the have the capability for infinite self renewal. They can propagate themselves indefinetly. Secondly, they are potent, in that they can differentiate into a number of different specialized cell types.
The two main types of stem cells are somatic stem cells (or adult stem cells), and embryonic stem cells. Somatic stem cells can be found in adult organisms, and are multipotent. This means they can differentiate into a select few cell types. By contrast embryonic stem cells are found in developing embryos, and are pluripotent. This means they can differentiate into virtually any cell type in the organism.
Both types are useful to scientists as they can potentially be used to treat or cure a wide variety of illnesses. For example, a common treatment for leukemia is a stem cell transplant from the bone marrow of a donor. Due to their ability to differentiate into many specialized cells, many scientists believe stem cells may one day be used to generate living tissue, which can then be transplanted on a patient.
Despite its potential use in medicine, the use of stem cells is controversial. This is due to the method in which embryonic stem cells are attained, through the destruction of human embryos. Many counties have laws which regulate this sort of thing. In Canada, researchers may only use stem cells that come from discarded fetuses from in vitro fertilization procedures.
Further information can be found here: http://en.wikipedia.org/wiki/Stem_cells