Article directories are websites that house free articles. These articles are usually put there by whoever owns the copyright to them as a promotion method. Each article has the owners byline placed under it so that those who eventually read the article will know who wrote it (or at least who owns it) and will be able to get in contact with or visit their website for further information.
Articles directories are a great place to put your articles so that they will make you money. By using this method, people who are interested in your product or service will see your article, view you as an expert in the subject, and will visit your website. Even if you cannot write or do not have any knowledge on the subject on which you are promoting (for example for you run an affiliate website), you can always hire a writer to do the work for you. Getting quality articles written will be expensive up front, but they will pay for themselves in no time, either through affiliate sales or selling your own services, and everything from then on is pure profit.
Let's take a real life example. Imagine that you are an accountant working from home. You write an article on an accounting topic and place it on various article directories. Those who are looking for the subject you wrote about will read your article, see that you have the knowledge and skill that is needed to do a job for them, and visit your website or contact you via e-mail. Your article just gained you a new client who may use your services regularly, but will definitely give you a nice profit at least once.
Furthermore, since you have posted it on a free article directory, others who have affiliate websites about accounting will inevitably use your article for their website. Since they must attach your byline to it, this will bring you even more exposure for every website that re-posts your article. This because you will be benefiting of off the traffic that they get to their website.
There are numerous article directories out there for you to utilize. Your bet best is to put a copy of each of your articles on every one for maximum exposure. It will eventually help to bring more traffic and customers to your website, which will lead to new orders and more profit.