In 2004, Barack Obama was only a Senator from Illinois who supported John Kerry and John Edwards on the Democratic Ticket for President. His purpose in the speech was to rally his fellow Democrats behind Kerry and Edwards to support their campaign for president and vice-president: "rise up in November, and John Kerry will be sworn in as president. And John Edwards will be sworn in as vice president."
His main claim was that Americans should stand united. He reiterates this idea in several ways, first pointing out that "There are patriots who opposed the war in Iraq, and there are patriots who supported the war in Iraq"--meaning we should not be having petty squabbles about whether someone is a "patriot" based on this single point, as all had reasons for voting as they did and the end result of that vote does not mean they didn't have the country's best interests at heart. He also says "there's not a liberal America and a conservative America; there's the United States of America." He believes that while our ideas of how to remain strong, fight terrorism, and help the needy differ, we all want what's best for America.
He includes (and emphasizes) the idea that it is our fundamental belief that "I am my brother's keeper, I am my sisters' keeper -- that makes this country work." Thus, he suggests that it is our responsibility to take care of those we don't know, but from this idea he quickly swings back to this: "It's what allows us to pursue our individual dreams, yet still come together as a single American family: 'E pluribus unum,' out of many, one." That is, we are a diverse society, but we all want what's best for the country.