It's the first stage of the presidential election process, when party members in each state vote for the candidate they want to represent them in the forthcoming elections. So, at the start, there may have been four or five republican candidates, but by the end of the primaries the local republican party members had decided they wanted George W Bush to represent them in the election against Al Gore.
Whether that was a good thing or a bad thing is another matter...
Anyway, that's how I think the presidential primary thing works.