In traditional publishing, if you find an article you like, you can send the citation or link to a colleague at another university. If the colleague's university subscribes to the database holding the article, and to that journal and year, then the colleague can access it. If not, the colleague may be able to access it from another database. If the library has no access to the article, then the colleague legally would have to put in an Interlibrary loan request. Once they have the article, they would not be able to make copies to share with their co-workers.
In open access publishing, you find an article you like, and you send it to your colleague. Your colleague, in turn, sends it to his coworkers. And the It continues. Open access encourages the easy and fast spread of information.
No barriers to your research = more people can cite your research. There have been many studies to determine the effect that publishing OA versus traditionally has on the number of times a paper is cited since 2001. There have been a variety of results. Some say traditional is better. Some say they are about the same. Most say OA has more citations.
One of the most common arguments for open access to research results is that we've already paid for it. For instance, Dr. A at University does research, which is part of his position, and something the university pays him to do. He then analyzes his results and writes an article on it (also part of his position and something the university pays him to do), and then sends the paper off to Journal. Then researchers at other universities review the article (which is part of their position), and then the Journal publishes it. At which point the University then has to pay the Journal to have access to his article.
Similarly, a researcher gets a government grant to fund a research project. He sends the results to the journal and citizens of the country (who's tax dollars funded his research) have to pay to access the article. In the US, government funded research must be open access: but not until a year after it is published. If citizens want to access the research while it is fresh, they have to pay for it, unless the author has chose to publish OA.