This amendment would ban all political parties from running for any federal or state political position. No more Democrats, no more Republicans, no more Green Party or Libertarian or Socialist or any of the other myriad other parties that are out there. You could be a part of a party, but you cannot run based on that party. IE: No D or R next to the name on a ballot. The person would also be denied any sponsership of a political party by disallowing them to even speak of any political parties what so ever in any capacity or situation.
Please note that these are not the exact words to be used obviously. This is just a gist.