Cellular material in plants is capable of differentiation in form of roots in presence of certain proportion of hormons called cytokinens and auxins.
This happens during entire life of plants, that at different times of plant life it is the hormons that carry messages at diff. plant sites telling plants when to flower,fruit and prepare for death (Scenescence).
Auxins, Gibberellins, Cytokinens, Abcissic Acid and Ethylene Gas are Hormons.

chiman

Specialized embryonic material called meristem tissue is capable of changing into growing points or form roots. As mentioned by charman, this depends on the presence of hormones.

You can refer to this article to see how it works:
http://www.suite101.com/article.cfm/18505/105386

Other articles available:
http://www.suite101.com/topic_page.cfm/18505/4966

Here is a link that might be useful: article

By the way, if you have space and some spare cash, you can mess around with plant hormones and enter the world of tissue culture.

Just like chaman was saying, auxins will cause roots to develop, while cytokinins will cause shoots to develop. If you adjust the ratio between the two just right, you can turn plant material into a strange-looking mass of undifferentiated plant cells, called a callus culture. This callus culture can survive and grow without light, if you grow it on lab media containing sugar and other nutrients. After it grows so much, you can divide this mass into little clumps. You then expose each little clump of cells to hormones, causing them to develop a shoot and then roots... and thus turn each clump into a small plant. The neat thing is that all of these plants will be genetically identical to the plant material you started with. This technique is called micropropagation.