Here is a very basic starting point to learn more about Anarchism. Unfortunately it seems the rich history of Anarchist theory and practice has flown over many people's head. No matter what you think of Anarchists, any basic understanding of 19th and 20th century American history will illustrate the key role's they have played in labor struggles, peace movts, women's rights, birth control, civil rights, ecology and the critique of corporate globalization.
For a more traditional definition try Peter Kropotkins: "Anarchism" (incidently this essay is the Encyclopedia Brittanica, perhaps a good next step from the dictionary) and "Anarchist Communism".
Then you could read some Emma Goldman and her essays on Anarchism and how it plays into a variety of social issues.
For a very easy to read and concise explanation try Alex Berkman's "ABC of Anarchism"
These days there is a wide variety of thought within the Anarchist "movement". If you want to know about the more radical strain, investigate 'green anarchism' or anarcho-primitivism theories and critiques. John Zerzan's "Future Primitive" or "Running on Empty" might be a good place for this.
Note these books are availble in the libraries and most good book shops. Try Laughing Horse books on 38th and Division. or go to www.infoshop.org and you'll soon discover how people who call themselves anarchists envision a better world.