This quote is the reason why we have freedom of the press. It is saying that words (the pen) are more important than weapons (the sword) in creating changes in the world.
To understand why this is, just look at what has happened in Egypt lately. There, words have proven to be much more important than weapons. We have seen protestors come together, drawn by "the pen." They have been drawn together by word of mouth, by social networking, and by the media. They have been drawn together because they believe in an idea--the idea of freedom. All of these are things of "the pen."
Against them, you had the Mubarak government. The government had all the power--they had the tanks and the guns and the protestors did not. But the power of ideas overcame the power of the weapons and the side with all the weapons ended up losing.
So, when you hear that the pen is mightier than the sword, it means that words and ideas are more important than force--more able to change the world.