Made during the his acceptance of the Democratic presidential nomination, it's a powerful line because Obama's presidency has been considered illegitimate by right wingers. He's Black, he has an international background ("birther" issue), he has a non Christian name (Muslim issue - which should be a non-issue since there's supposedly a separation of church and state), and did I mention he's Black. So, when Obama made his, "I'm the president" remark," it was to confront discrimination that is still allowed to exist in the U.S.
Just because there's a black president in the while house, it does not mean we're in a "post-racial America". It's a fantasy perpetuated by the liberal left as proof that we've arrived as a tolerant nation. It's also a tool used by the right to ignore present racial injustices in order to further discriminate people of color.
So, yes, Obama, you're the president. Now that you've fully been pressed to the ground by the boot of intolerance, maybe you too will finally abandon all ideas of a "post-racial America" and get up to fight the continuing battle for equality and justice for all.