A fallacy is faulty logic. People commit errors in reasoning sometimes from ignorance, sometimes willfully (to deceive) and sometimes unintentionally. It is important for you to know something about fallacies so you can be on the look out for them as you critically evaluate the arguments of others, and so you will have more to say when you refute them. Learn these common fallacies by looking up definitions and taking notes on the examples provided here:
The Fallacy Files (this site may be accessed also from my Rhetoric Ring links.)
Use the search engine you find there (select "www.fallacyfiles.org" to search only within the site) and simply input the names of each of the fallacies listed below.
One more I want you to know, that isn't covered at the Fallacy Files for some reason, is Non sequitur which means "it does not follow." This is an illogical leap.