Improving organic search results: Submitting articles is one of main method for generating one-way back links to your site, which increase your page rank and link popularity. A high quality articles can be republished on multiple sites, so you automatically get thousands of links pointing back to your site which will increase your position in the organic search results and getting found for more keyword searches.
Increasing traffic: Article submission can help to increasing traffic from related sites. If you have an article with valuable content, many people will read it and even spread it. Therefore, you will be able to reach more people and this thing becomes viral in nature. Reaching more people means generating more traffic to your site.
Building incoming links: Most of article directories accept your article with link that pointing back to your site. They allow links in author resource box of article submission form. You can place up to 3 links in author resource box. One of main benefit is that you can include any kind of links such as your site home page link, deeper/inner page link, blog link, article link, etc in that box.
Making site more useful and unique: Article submission is one of best way to help to educate your readers on particular topic of your field. If the article is unique, interesting, and useful than you can attracting new and unique visitors to your site.