There are millions of Americans outside Washington who are tired of stale political arguments and are moving this country forward. They believe, and I believe, that here in America, our success should depend not on accident of birth, but the strength of our work ethic and the scope of our dreams.

This quote is saying that many Americans living outside of Washington D.C. are tired of the same arguments about politics. Instead, they (and the speaker) believe that a person’s success should not be based on the family they are born into, but on the effort they put in and the goals they set for themselves.