A primary election is an election run by the state government and created and organized by state law, just like any other election. In a presidential primary, the voter either votes for the presidential candidate by name, with the results being used to determine which delegates are elected from the state to attend that party’s national convention, or he or she votes for a slate of delegates directly who are either pledged to vote for a particular candidate or are pledged to be uncommitted as to which candidate they will support at the convention.
(This is very similar to the way we vote for president in the general election – our votes in the name of the candidate actually are used to determine which slate of electors are chosen to vote in the Electoral College for president.)
Often the state must grapple with the question of whether to hold other primary contests, such as for governor or representative to the U.S. House at the same time. A primary held in, say, February (like New Hampshire) may be favorable for the state having influence over the presidential nomination, but it is very, very early for legislative or other campaigns to begin and puts challengers to incumbents or candidates for open seats (in which no incumbent is seeking election) at special risk. Some states settle for a later and lesser role in the presidential campaign to benefit those interested in these other offices, or it will do both and pay for the expense of two primary elections. (North Carolina has gone back and forth with its primary date in recent presidential election years on just these grounds.)
Or the state can simply choose to let each party decide who its delegates will be. The standard way of doing this is to use the caucus-convention system -- that is, to hold what is actually a complex, multi-stage event. We short-handedly refer to it as a “caucus” because its first step is to hold a set of local caucuses. But this simply starts a process, whereby those in attendance at the local caucus (often at the level of a precinct, or neighborhood, level) select people among themselves to be delegates to a convention, perhaps at the county level. That convention might select nominees for county-level offices and also will select delegates to the next level of convention, perhaps at the geographic level of a congressional district. That convention will also select nominees for appropriate offices and delegates to the state-level, where, at last, delegates to the national convention will be selected.
One of the major reforms of the McGovern-Fraser Commission was to require that caucuses be open to all members of the party in the public. And it may be open to more than the party in the public, too, such as independents, because parties typically don’t have an actual “membership.” In practice that is usually defined to be anyone who is willing to declare openly that they are a member of the party.
The caucuses also had to be timely (in 1968, the year the commission was appointed, more than a third of the delegates were chosen in 1967). And, perhaps most importantly, delegates to the next level (and then the next level, etc.) had to be in some way proportional to the presidential choices of those attending the caucus.
Caucuses typically attract very little attention, Iowa is unique in that regard, because it is the very first event in the nation. And attendance of even 5-10 percent of eligible Iowans is considered a good turnout. In other caucus states, there is less attention and less interest, so turnout is even lower. That makes the problem for the presidential campaign one of trying to find those very few who can be convinced both to back their candidate and actually to attend the caucus.
Turnout of supporters is the big problem to solve, as primary elections also do not typically attract high levels of turnout. Turnout of 25 percent is good for one of the highly visible primary elections.