The word стол means 'table.' It is one of the first words taught in Russian classes because it is short, easy to pronounce, and has perfectly regular grammatical endings. It is also the classic word used when practicing noun declensions: it's common to hear Russian students chanting стол, стола, столу, стол, столом, столе in the course of their studies. Declining стол out loud gives the good Russian student the same pleasure that a good piano student gets when practicing scales. Sure, it's a simple thing to do, but it shows a type of mastery.
There are two different patterns common to declining Russian nouns. The chant shown above follows the classical order that is used in reference books in Russia and in more traditional textbooks in the United States. There is a also another pattern, the 'linguistic' pattern, that is used by historical linguists and by newer textbooks. The newer system is better pedagogically because it illustrates the generalizations of noun declension in a neater fashion. You can see the two patterns contrasted here.
The phrase письменный стол means 'desk, writing table.'
Don responds: Very nice! For American readers I would like to point out that the order of cases that vio mentions here is the one used in most Russian dictionaries and textbooks. In this blog declensions are presented in the linguistic order.